Correct. It is similar to pushing a box with friction opposing the push. You do work with your own force F_p as you move the block, while the ground also does work in the OTHER direction (different signs) with the frictional force F_f doing work as the block moves.
If considering air resistance, then the net work is not the same as the work done by gravity, which is the same regardless of air resistance.
Your notion of W=F*S works if you treat gravity as an approximately constant force, but that approximation becomes poor as S gets larger. This all...