I suppose not; the rules mention that you have to use at least one copy of everything in the FG deck. Fortunately, I think that's only Dark Matter (gravity), Serket (life) and Dreamcatcher (entropy), which should leave tons of decks still available for use.
Question: You mention we can use each FG twice. Do I have to run the same decklist each time? For instance, if the false god dragonsdumbisme, whose deck contains 30 quantum pillars, 15 flooding, and 15 miracles, is the one I want to use, can I run in game 1 24 quantum pillars and 6 floodings, and in game 2 run 6 miracles, 2 floodings, and 52 quantum pillars?