I had a piece of driftwood floating in my tank for a year. Kept thinking it would eventually sink. Kept thinking one day it'd sink and mess up the aquascape. Kept floating. It was sort of neat, until one of my hatchets jump up on top of it and I didn't realize until it was too late.
My guess is that the wood should be dry before glueing, but read the instructions to be sure. The driftwood that I've bought is attached to slate by a screw. If you have a drill, drill a hole in the slate and screw it to the wood. However, you might want to use a glass bit or possibly a concrete bit to prevent cracking the slate.