If Luffy joined the Marines, he would work directly under Garp and be sent to Headquarters, and if he ever went on missions, it would be to track down pirates or protect royals. He won’t go all the way back to East Blue, and he wouldn’t go all the way back to Paradise.
Let’s check the possibilities of other members of straw hats if they didn’t meet Luffy.
Usopp
Let’s start with Usopp. If Luffy joined Marines, then Usopp would be gone. If he got in Kuro’s way or found out what he was planning, Kuro would kill him.
If Luffy joined Marine, then what does it mean for Nami?
NAMI will probably be under Arlong’s control for the rest of her life, or at least until the dragon comes crashing through that area and frees them from the corrupt marines. They did say that there were marines strong enough to help beat Arlong, but the marines never had a decent reason to dispatch one to a rural island in the middle of East Blue. So there would never be any help.
Buggy
Buggy would have still been messing around, and maybe he would have killed Nami after she proved she wasn’t as bad as they thought. That would have been the end of it.
Pirate Hunter Zoro
Morgan was going to kill Zoro, Or maybe they got into a fight. And probably would’ve killed Zoro. But even if he gets past Morgan, marine captains will be after him because he just got away and destroyed a whole base. That would piss off Marines.
Dr. Chopper
Chopper would still be under Wapole’s control. Wapole would never lose power. Even so, Teach would have attacked it and destroyed it.
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Crocodile
Crocodile would have killed Vivi, which would have been his plan, and if Smoker had tried to stop him, he might have been caught and killed. Of course, they would send a real vice admiral to deal with Croc at some point. Tashigi would have never been important because she, too, would have been killed by baroque works. Alabasta would become a terrible place.
Monkey D Dragon
Dragon would find it exciting and a little sad that his son is moving up in the marine ranks and that he might have to fight his own son one day. The same goes for sabo. Considering how angry and disrespectful of authority Luffy is, he could be demoted a lot or even end up in the brig.
The whole thing with Moria?
Well, Moria just hangs out on that island until he’s called up to fight as a warlord again. He probably wanted to fight Kaido again someday, but that won’t end well, so Moria will probably die.
Robin
Well, With Robin, she would have kept looking for poneglyphs, and with Crocodile, she would stay as long as it was helpful. If Crocodile somehow got captured, then she would have fled with someone stronger, probably with Aokiji.
Frankie
Frankie is sent to impel down. CP9 would be sent on a different mission after being called back.
Skypiea Arc, Enel
Enel would have finished his plan and left if he had Skypiea. He would be God of Skypiea. Only a few handfuls of people could go toe-to-toe with him without Luffy’s gomu gomu no mi.
Doflamingo (Mingo)
Doflamingo would keep Dressrosa under his palm of a hand, and if there was a rebellion, it would probably be caused by Law, and the rebels would be killed, and the Law would be dead.
Hody jones would have kept trying to take over Fishman Island and kill the royal family.
Vinsmoke Sanji
Until Mihawk vs. Krieg, Sanji would have been an unimportant cook, and since he never became important, he wouldn’t have been picked to marry Pudding.
Brook
For the rest of eternity, Brook would do nothing at all. To pass the time, he would sing songs and ask for the panties of dead people. Lol.
Coby
I think Coby would have stayed a helpless puppy if he hadn’t met Luffy. HQ is a thousand miles from where Luffy is. Morgan would never have been caught that far out, though. His iron boot would stay until the army of the dragon came.
Mihawk
Mihawk will keep being the best swordsman.
Emporio Ivankov
Ivankov and his team would have stayed in prison for a long time, but eventually, they would have broken out with the help of the Revolutionary Army.
Kin’emon
Kin’emon and his team would have never met Luffy if he had joined the Marines. Saying this, the whole Wano Arc would have been affected by this.
And that’s about it up to the point where the timeline is right now. We can’t guess about future plots and events because nothing big has happened yet.
Marineford probably goes the same way, but Luffy and Garp aren’t sure which side they’re on, so they stay out of most of the action.
As for Luffy’s power, he wouldn’t have eaten that fruit if he hadn’t been talking to Shanks when he did. I think that for this timeline to make sense, he can’t meet Shanks and can’t go to their island.
Luffy would learn a fighting style that is kind of a mix between Lucci and Garp because his natural talent would be around Lucci’s level, if not a bit higher. Depends on how many dangerous fights he gets into. If Luffy fights a lot of pirates, his skills will go through the roof. But, as I said, I don’t think he would have been promoted to Admiral or even Vice Admiral because of how disrespectful he was. He would learn Haki much sooner, too.