Those bolts are what holds your AC unit on. As long as you don't move it around, you should be able to thread them back in without any problems. Between the AC unit and the roof is a gasket; when you tighten those bolts they compress that gasket, providing a water tight seal between the AC and the roof. Too loose or too tight and you'll get leaks.
Once you remove the lower section of the AC unit you'll be able to see the ducting more easily. In most cases this ducting is nothing more than a tunnel created by the removal of insulation in the roof. Rather than installing luan as a stiffener, you might consider a similar thickness of styrofoam sheet. It'll be lighter and won't reveal a wood grain "print" in the headliner when the two are glued together.
2014 Coachmen Catalina 253RKS
2017 F350 6.7L DRW CC LB 4x4 Lariat