The brackets that hold a shower head on the wall are screwed in place with an ordinary screw. So the walls are obviously thick enough to hold a screw.
Not sure I'd want to add a screw into a shower wall, but if you plan on the holder being there "forever" it should work. You could always add a dab of epoxy to the threads for extra holding power.
The bracket for our shower head was coming loose. I found that whoever put the screw in over-tightened it and stripped out the hole in the fiberglass. I simply drilled a new hole next to the original one and carefully tightened the screw back in. Gets very little water spray up that high and wasn't worried about using anything to help seal the penetration.