I suppose it should. It will be even slower than it is when upped, so expect some really long games. It will lose more often, but I think you should be able to earn more on average than you spend on initiating battles.
When I created the deck for the first Time, I think I had about half of my cards upgraded (after selling the SG-rainbow deck I used earlier to grind FGs), and I somehow worked my way up to upgrading the whole thing.
Keep in mind though, that I haven't tested that deck against the newest False Gods, and it was designed even before Dune Scorpions came out. After Dune Scorpions arrived, I tried modifying the deck to use them and supernovas to speed up the deck, and it worked, although I'm not sure if it improved the winning ratio or not. Definitely though, that version required more upped cards.
Anyway, right now I'm not playing Elements anymore, only visiting the oracle and forums everyday to see if anything interesting is going on, because ironically I don't have enough Time... so my knowledge might be slightly outdated.
Best advice I can give you - try it, and if you have any ideas to improve it, be creative!