I'm about to install this acrylic/fiberglass shower base. It's going on top of a wooden subfloor, with 2x4 walls behind it, then tile on the walls. The instructions that came with the base say to lay down a bed of mortar and set the base on top of it, with the flange right against the studs; they don't say anything about screwing the flange to the studs, but I've seen it done. Would the screws be overkill?
I wouldn't put holes there unless you carefully waterproof them and are 100% sure they won't show. Some panels don't sit down tight on the bottom. You'll also want to be sure not to crack the flange if it's not tight. Use shims if needed.
The mud base, floor caulk and plumbing combined will keep it from moving.