Another question I have is by how much the motar bed may raise the tub
off the floor. I roughed in the plumbing already, and I roughed in
the drain pipe based on the tub sitting on the subfloor. Because of
limited access, the drain was not fun to do. Therefore, i don't want
to end up re-plumbing the drain if the tub will be raised up off the
floor some from the motar bed.

As to the use of drywall mud, instructions specifically say NOT to use
drywall mud:

"IMPORTANT! Mortar cement is required to level an uneven subfloor. Do
not use
plaster, gypsum cement, or drywall compound for this application, as
these materials
do not provide adequate structural support. Spread a layer of mortar
cement on the subfloor where the bath supports will be
located."