I think some people may be confused on the dynamic between Get Back/Let it Be and Abbey Road. Get Back was an album that was Paul's concept; he wanted to get back to basic rock and roll, and didn't want George Martin and his production to oversee it and overproduce it because he wanted core, basic rock. I think it was because he thought if the Beatles could get back to that, they'd find themselves again and stop arguing. Problem was, the sessions weren't very productive. Don't get me wrong, they produced hundreds of hours of tape and hundreds of songs, most of which have never seen official release (albeit keep in mind many were just messing around), but they were more like sketches and rough drafts than finalized takes in many places. And the sessions eventually broke down. The Beatles would hand things over to producer Glyn Johns to take the hundreds of hours of tape and make something out of it. He produced two acetates, neither of which the Beatles were happy with.
The band eventually walked away from the project, and put it on the back shelf. Out of that chaos, Paul went back to George Martin and asked if he could help them make a new album and just get back into things. That became Abbey Road, and the songs from Abbey Road were, in many places, songs that had been demoed or worked on for Get Back. So basically, Abbey Road is like the version of Get Back that actually worked if you wanna think of it that way. The good twin compared to the bad one. And so while Get Back/ Let it Be was worked on first, Abbey Road was released first, so really, Abbey Road was the last real Beatles album.
When the Beatles were really on the rocks after Abbey Road, Allen Klein went to Phil Spector to take the failed Get Back sessions and make an album out of it. The album was renamed Let it Be, and Spector took songs and overdubbed them with orchestral backing and filtered them through his Wall of Sound, and it was released in 1970.
If Get Back is released before Abbey Road, as it was intended, its effects depend on what happens, whether the Beatles are happy with one of Glynn Johns acetates or George Martin manages to oversee them, or the sessions are actually successful. I think the former option would be most likely. Really, Phil Spector's version of it wasn't much different except for the backing orchestras and all that, which made a huge difference sound wise, and undermined the spirit of basic rock that was the project's intent. The John's acetates preserve this. I think the reaction to this album from the critics may be much the same as Let It Be; that it was ok. And later opinion would then improve.
Another effect: Paul McCartney listed in his reasons for leaving the Beatles that "The Long and Winding Road", which he meant to be a simple piano ballad, had been ruined by Spector's overproduction, and this infuriated McCartney. If either of Glyn John's acetates was accepted, this would not have happened. So perhaps this would ease tensions.
If you haven't heard either of those acetates, I suggest finding them. They're basically Let it Be without the backing stuff, which I think it better.