If you're talking in terms of system specs, gmod will run fine if you run TF2 fine. If you're talking in terms of the one source game requirement, I don't foresee a problem.
Also, the only thing you need to worry about in terms of mod compatibility are mods that use files from other Source games. Fallout isn't on the Source engine and isn't made by Valve so unless the mod creator used any script (you'll get LUA errors in the console), texture (pink and black boxes), model (ERROR model), or sound (no sound will play) from a game that you don't own or have mounted, you'll be fine downloading whatever you want.