Q:

Can I sheetrock over styrofoam on a garage ceiling? 

I am buying a home with a detached garage that the original owner insulated.   The garage is probably 25 years old.  At the time of construction, 1" expanded foam was nailed directly to the rafters to insulate the ceiling.   Over time, the foam has shrunk (and deteriorated to some degree) leaving 1/2 - 1" gaps around all the seams and is not sufficient any longer.   The attic is vented properly. 
I would like to re-insulate the ceiling with standard blown-in fiberglass or cellulose.   I would also like to sheetrock the ceiling to provide a better finish. 
Can I install the sheetrock over the existing styrofoam and then blow in the insulation in the attic? 

A:

Yes you can sheet rock with longer screws.   However the screws will basically have no hold until they hit the wood.   Your previous insulation will continue to shrivel.   Your ceiling will sag (glue and screw your drywall to ceilings).   And you will be like - "why didn't I prep this for a couple hours so I don't have to redo it."   Nothing worse than completing a job and knowing that something you did could (probably will) go wrong. 
Also I doubt your insulation is even/flat and I think this would make hanging it flat very hard. 
I am all about saving time but if you are in the house for more than a year or two I think you are wasting time. 
Also why are you insulating the roof of a detached garage?