In case anyone had the same question and is wondering, a simple experiment yielded success.
Placing modded files into the "mods" folder (whoda thunk?) within GOG's Saints Row 4 folder -- and nothing more -- seemed to apply them exactly as needed.
Specifically, both a texture mod as well as an early-unlock mod worked as intended and seemingly without issue (was able to play, save, load, and keep playing without any obvious problems).
I wouldn't go as far as to say it'll definitely work for all mods across the board, especially as these are very simple mods, but it's a good sign.
Hopefully this helps anyone who had the same question!