Would it work if I prime only a partial height of a painted wall?
Just to answer a rather odd question the way it was written...
No if you plan on going to specific height and stop right there all the way around.   You will create a paint seam and it might take a few coats to make it less noticeable.
Yes if you kind of go to a height and taper off randomly on both side of the height with less paint/pressure as you go up.
My advice would be to cut corners, in the corners (and to get more people to help).   You can prime pretty quickly - and paint - open walls.   If you are not worrying about the ceiling or edges painting is twice as fast.   I would suggest you prime to ceiling but start tapering off as you go up and the top 6-8&quot; need very little.