Can I dry out insulation behind drywall?
Everything depends on the degree to which your insulation is wet. 

I'd cut an exploratory trench about 6" wide across the entire width of the affected wall, both top and bottom. (Don't cut right into the ceiling corner -- stay a few inches down.)

If everything is wet, just keep pulling the drywall down. (It's not that hard to re-rock...) 

If everything is just a tiny bit wet, leave the channels open for a while and check periodically. 

If you're in doubt about what constitutes 'a tiny bit', I'd suggest you err on the side of demolition. Mold is not your friend.