The only benefit I can see is that it adds a protective coat in case you get any light moisture on it. The paint might shield it some. (but of course not completely).
Drywall loves to soak up moisture. (especially w/o paint)
moisture attracts termites.
termites... well you know the rest.
I doubt it will add any "value" to your house having it painted, but it might add some garage "curb" appeal to the next potential buyer.
You're only looking at a couple buckets of primer for $10-$12 each and a few buckets of paint for $10-$20 each.
or skip the primer and just use an exterior category of paint for the garage. Exterior paint is typically a little thicker and made to stick better than interior paint. Often exterior paint has a mildew additive. If not, you can get the paint store to add it. Since the garage is prone to more moisture than inside, not a bad thing to add. Using a bathroom specific paint will have moisture/mildew additives also.
Since exterior is thicker also, you can prob get away without having to do a 2nd coat also.