To see if the glue warrants removal, check your walls with a straight edge, 4 ft. minimum, longer if you have one, make sure it is straight. With that check the top and bottom plates for straight, then check each stud face with the straight edge too. Lastly check across the studs horizontally at the center. Another alternative to a straight edge is string lines with a spacer block at each end, but takes a little longer to set up. If you have everything cleaned to where the thin layer of paper front the back of the drywall is left, that is all the cleaning needed. If the differences between faces are more than an 1/8", trim the tightest spaces back until the gaps are uniform.
If everything is within an 1/8 of an inch the drywall, with screws and new glue behind it, the drywall will readily stay, as you may have noticed when you removed the old drywall. You were accurate in your observation, there are enough screws to hold it until the glue dries.
That can be a good thing or a bad thing. The good thing is, drywall has a tendency to lay completely flat if there is nothing to keep it from doing so. Because of this it can span over slight differences between surfaces, that's what the glue will do, provide a "filler" for the gaps behind the drywall.
The bad thing is, it can also, with a minimum of obstruction, bow away from the wall studs, the biggest culprit being, cutting the sheet too tight between other surfaces or getting it to close to the floor, it should be about an 1" above subfloor, 1/2" above an existing finish floor. This is so any trash or small debris will not get trapped between the framing and drywall.