There's no evidence to show that it wasn't impossible for non-trapped players to gain access into the game. What Kayaba Akihiko did was removing the "Log out" option and altering the game so that the death flag would cause the NerveGear to fry the player's brain.
Of course, whether it was possible or not on the basis of what Kayaba did to the game is one thing, the other factor to consider is the authorities.
When Kirito first entered Sword Art Online, he was on his bed. However, at the end of Aincrad arc, he woke up in hospital as seen where he wakes up and stumbles out to look for Asuna.
It was also mentioned that the NerveGear has it's own internal battery in it which accounts for 30% of it's weight, in the Novels it's revealed this battery has atleast 10 minutes of power in it being one of the conditions set to kill a player.
In the novel, Kayaba announces to the players that if one of the following happened: being disconnected from a source of electricity for 10 minutes, cut from the system for more than 2 hours, or dying in-game, the NerveGear would fry the player's brain, killing them in the real world.
Kayaba also says how people outside the game were told to avoid forceful removal of NerveGears yet some chose to ignore this (though it doesn't imply he cared for their lives).
Having informed the outside world of the situation beforehand, [Kayaba] reported that friends and family members of some of the players had already ignored his warning, causing the death of 213 players, showing images of the SAO incident.
Also every trapped SAO player was moved to hospitals within the first 2 hours of the game starting as a respone to Kayaba's announcement to monitor their condition, and for those who didn't die in-game, to keep them from becoming under-nourished.
He also told them that his crime was being broadcast all over the world, with the location of each player, thus the authorities would be moving them into hospitals to put them in better care during the 2 hours he had allowed the players to be disconnected from the system.
all of this indicate that the Japanese Authorities were well aware of what was going on and would be in the public's best interest to prevent any more cases of players being trapped inside. in terms of the game the Authorities didn't need to stop people getting more copies of the game as only 10,000 copies were first produced and 10,000 players were trapped1
Only 10,000 copies were printed in the first batch of the game, and online sales sold out within seconds. Hard-core gamers waited in line for days to purchase the first few hard copies from many stores.
«Sword Art Online» officially started server service at 1 PM of November 6, 2022 and obtained infamy when the creator succeeded in trapping 10,000 people in the game, and making it so that death in-game would mean actual death for the player.
however on the NerveGear Wikia page it states there were about 200,000 players in possession of a NerveGear, so i assume that the authorities seized about 193,853 NerveGear during Death Game (3,853 from the player who died)
This next part is mainly speculation. However, Cardinal system, which could possibly corrected new players entering the game, since we didn't see outside authorities trying to help players in-game with clearing all 100 floors. though this could be them being cautious as effectively Kayaba was in control of 10,000 lives
It is also mentioned that Kayaba has a level of honor and fairness so i would assume that as he aided players to reach the 95th floor (where he would reveal himself as the final boss) he would also act on any outside interference against anyone in some way if they came up with hacks designed to help beat the game or attempt to back into the game itself.
Akihiko had a level of honor and fairness. He designed Sword Art Online to be a beatable game by anyone who had the skills. He never interfered with the players' progress to keep them from advancing through the game; in fact, as Heathcliff, he was actually fighting on the players' side, helping them clear floors. The one exception to this is the fact that he made himself invincible until his battle with Kirito, although this was necessary to survive the game until the 95th floor was reached, where Heathcliff planned to reveal his true identity and become the final boss on the 100th floor.
The answer are in the first episode of the series. Only 10 000 copies of the game are sold, and all of them are in use, because in the presentation, when Kayaba told her all of the "new rules", there are more than 9k players online, and some are dead at this moment.
Also, I can understand other explanations are correct, because yes, probably the "login server" is down, or there's only a hidden server (neither series nor the novel said anything about if Kayaba can logout or not).
@Quikstryke: They cannot hijack packets of the server. I explain: all these players are in controlled environment, because of this, you can sniff the information between NerveGear and the servers. But, you don't know the use of these data. When you do a sniff on an MMO, you are playing the MMO itself. Because of this, you view a packet going to the server or from the server and the effect of this packet on your screen. If you receive a bunch of packets, but you cannot relate it with the proper actions on the game, all these information are more or less useless. More, if these information are encrypted. If you have 5 packets, for example, you can try to relate itself with actions (for example doing one more time the same action for view common packets). But, if you have thousands of them, you don't have nothing.
I came here because I wanted to know people's opinions on the matter. You are all sticking to the fact that only 10,000 copies were made and all were being used. While this is true, I think that we shouldn't go on facts for this. I believe we should theorize and just get away from the fact that all copies were in use. Let's say that about a hundred or so never logged in on the first day. Would they be able to log in if they still had the copy of the game? While we are at it, let's take away the whole thing about how the government would confiscate those copies as well. Also, let's put people's reasoning about joining a death game aside.
So my answer to this is kinda going to be everywhere.
Alright, I believe that in a way, they could. I mean, look at how the game was set up. Let's start with the Beta of SAO. Everything is great; a few bugs here and there, but everything is running smoothly. Now for the Full Version. The game was specifically modified to not have a "Log Out" button. So the people that joined SAO on day 1 already logged in while the game had no "Log Out" button in the first place. So there goes that theory about people not being able to join after the "Log Out" button was removed. Right now it's looking as if they might be able to. Now let's go into the game's system, Cardinal. The Cardinal system is SAO's whole system and does a number of things. It would also adapt to situations. Let's say one of those things is to make the game fair for everyone. Would it not block out any other people from entering because everyone had a head start? It would possibly try to send them to another server for when the game had multiple of them. But then what about the Beta Players? They are ahead of everyone; would that not be the same as if someone new joined? So there goes that one. It would go without saying that nothing is standing in the way of a person from joining. The servers wouldn't be full, so people could still join. Unless the guys that worked on the game made it so that no one could join. But with that said if they had that power to do so, then wouldn't they be able to pull everyone out of SAO? It's most likely that Kayaba was the last person to check the systems before release, so he could have made changes to the game that the others didn't notice. Or maybe Kayaba was the last person the game went through before release so everything would be set up the way he wanted it to. It would also go without saying that only Kayaba could access the game, as we learnt that he was actually playing himself. Now, there's another thing we have to consider. I believe Kayaba would not have joined SAO on day 1 either, other than his appearance at the opening ceremony. I believe that he would have joined after the first month or so to ensure that everything was going well without him interfering. Also, what's to say that Kayaba thought about people not joining on day 1 and didn't bother to put a restriction on it? He did want everyone to join so that he could control a world by his design. So the reasoning stands that yes, they could join and be trapped there like the others.
That's my theory, but something else bothered me as well. For this, I am bringing back the rule about the government confiscating the copies. If these copies of SAO were usable, would the government not try to find a way to get everyone out by looking at the game's codes and crap? This was most likely a thought in Kayaba's mind. So he probably did put a restriction on new players joining. Now with that in mind, Day 1 would have been the only time to join, unless you're the GM. Joining on any other day would result in a connection problem. So if we add in that one little detail, then the whole answer turns around. So it varies on different occasions, but my final answer is no.
Now don't go hating on my theory as this was actually my first theory that I have thought of myself. And I'm sorry in advance if any of it does not make sense as it is very late so I'm tired and I've spent like over an hour writing this.
@Azrael response is the proper response to this, but regarding whether they could or not outside of the initial units and other units were confiscated, Kayaba probably closed off the system/server since Govt or someone could hack in or hijack packets if they wanted to (happens now with MMOs). Even Sugou who wanted people for test subjects could only do it when they logged out which means he couldn't just penetrate the server and was waiting for it to open up to reroute 300 people to his own.
To add to this the new units in Fairy Arc were already in production and couldn't physically fry anyone's brain. People would have just used this to log in and communicate with those who are trapped but that never happened.