No do not use the stud adhesive as cornice cement.
The screws need to be slightly imbedded but not to break the paper. If they are above the surface nip them up until they are just below the surface.
If the screw breaks through the paper you WILL need to put another screw in beside it, fixed to the correct depth otherwise you will get popped screws heads.
Jayson, the stud adhesive will theroetically stick the cornice permanently, however it would be a cow to clean off the execess and you would need to pin the cornice in place as the adhesive takes 24hrs to dry. Personally I could not think of a worse way to put up cornice!! No more nails and any adhesive will also do the job but you dont see people doing that for good reasons. Chuck the stud adhesive and spend 20 bucks on a 10kg cornice adhesive, and save yourself some grief.
Cheers Rod