Multiple Installations of MTW:VI?

[Etym]

Would a saved game from NTW, for example, show up next to a save game from a vanilla MTW campaign?

Since each folder (MTW "clean", NTW, XL, etc.) has its own "saved games" sub-folder, whatever games you save while playing that mod should go into that mod's saved games with no mixing. Be careful about moving saved games around between the mods, however. They'll likely cause a crash if you try to open, say, an XL game in NTW.