The answer is yes (there's a tldr; at the bottom if it's too long and boring for you).
Just to clarify, my answer is a mixture of evidence and speculation. And it goes more in depth. And it assumes that you are talking about Konoha (not the other villge where they kill each other to graduate).
Entering the Academy
^ In episode 419 (Papa's Springtime of Youth), it shows on the bulletin the names of the people who made it into the Ninja Academy. If you count the number of names, there's 34 of them. Not counting Might Guy, who couldn't find his name.
[I can't find this image. When I do, I'll post it.]
^ In this image, two more people are allowed to graduate, which includes Guy. This suggests, although not proves, that the Academy requires a fixed number of students in the Academy every year — in this case and time, 36.
Graduating from the Academy
From the image below, it implies, from Kakashi's words, that only 27 of the 36 students can graduate. That's a fixed 75% pass rate, meaning that no matter what happens, there will always be students who fail. And their performance in the exams is relative to each other.
Becoming a Genin (Teamwork Test)
Again, from the image above, it states that only 9 of the 27 graduates can be Genin (33%). This means taht there will always be exactly 3 more new teams, each with 3 Genin, at the end of every school year.
Since only 27 people can graduate and 9 people can become Genin, there will always be 3 teams, each with 3 people. Naruto not graduating just means that another person would have filled his place (that would make for an interesting alternate story).
The use of multiples of 3 (i.e. 36 can enter, 27 can pass, 9 can become Genin) greatly hints to the fact that all of this is intentional.
Oh, and by the way, graduates who don't become Genin have to go back to the Academy. Iruka may have helped Naruto, but at the cost of another student. Talk about sympathy/favoritism/nepotism (okay, I'm being harsh).
What a long post. If you have any questions, ask. I did my research.