I mean, I drag/drop doom.wad, doom2.wad, tnt.wad, plutonia.wad, chex3.wad, freedoom1.wad, freedoom2.wad, hacx.wad, heretic.wad, hexen.wad, hexdd.wad, and strife1.wad onto the GZDoom exe without issue
The reason those work is because those are all vanilla Doom data and don't redefine any of GZDoom's cvars (console / user config values). The error you're getting is GZDoom saying that you're trying to define the same cvar twice, which you'd definitely get if you're loading doom_complete.pk3 as both an IWAD (as defined in your gzdoom.ini, which gets set when you pick an IWAD from the pre-launch window) and as a PWAD (by dragging it onto the EXE, which GZDoom always interprets as "load this WAD as an addon").