Before I begin to answer please let me state that I only watch the anime, I do not read the manga which is far ahead of the anime.
So the short answer is yes it is a possibility, however the likelihood I believe is very doubtful.
Gol D. Roger started the infamous age of pirates by saying his treasure was up for the taking and ever since then the military has been falling all over themselves trying to round up those pirates; it got to be so bad that they had to recognize some of the stronger pirate groups as "Warlords" who they would not go after for the piracy crimes in exchange for the Warlord pirate group to take care of the lower class pirates running rampant. Admiral Fujitora is personally against the notion of allowing the stronger pirates such as Don Quixote being allowed to do whatever they please and he wants to bring an end to the entire Warlord system.
The show is centered around the Straw Hat Pirates who have taken the world by surprise time and time again for how rowdy and badass they are. They went from defeating a small marine base to taking on the warlords, they went from warlords to storming Enis Lobby and giving a middle finger to the world government, and is if that wasn't bad enough they then took on the Celestial dragons who are considered gods compared to everyone else and then Luffy went and broke into and out of Impel down which just pub stomped the Marines reputation for being able to control the order. The straw hat pirates have made the warlords, the world government, and the pirate emperors their enemies, it is quite literally them vs the entire world.
The government is so busy trying to regain their diminishing reputation that they cant afford to waste time looking for pirate treasure. Remember the war of the great? Remember Whitebeard's last words? Whitebeard reminded everyone that One Piece exists to spark the flame once again because the government refuses to accept One Piece even exists. Imagine the government turning up with One Piece after all of this, it would bring humiliation on them; they would much prefer One Piece never be found and people losing faith in its existence as to make people lose interest in being pirates because the second they get One Piece and word gets out it'll just cause an even bigger wave of pirates but this time they will all be hell bent on going after the Marines directly and before you know it we have another war of the great.
Again this is all speculation and I have just as much evidence to support my theories as does the next guy to reply who says that I'm entirely wrong. From the way the series is going I expect that the main focus will be taking down Kaido and Big mam but we cannot forget about Luffy's wrath for Blackbeard; either way we all know the marines aren't even in the picture, its the pirate emperors that own this series. All it took was Shanks saying stop for an entire war to end, that's how terrified everyone is to piss off an emperor, and Luffy has made it his goal to piss them off. At this point the marines are relics of a lost age.