What are these thin boards resting on interior wall top plate for?
You're correct. They're just drywall backing where the span from the adjacent truss is too great to let it float. 

The drywall will not fall. You can remove the backing and the wall. When you complete your re-framing you'll need to add backing back in where appropriate. 

If you're simply removing that wall, do the demolition, then float boards on each edge of the drywall (half inch plywood or one-by lumber work well), screw them in place through the drywall, then add your 3-1/2" drywall filler strip.