So how does Pokémon Bank work with the Loto-IDs? Will the lottery game check the mons you have stored in the bank or will it only check the mons you have stored in-game?

Curious to know because right now my PC is just filled with every shitmon I've ever gotten on Wonder Trade. I don't want to release them because I want the trainer IDs to increase my chances in the lottery. But if I can put then in Pokémon Bank to free up some space in the PC, without hurting my chances in the lottery, then that'd be awesome.

Anyone know? Picture unrelated.