I've been considering restarting my save and replaying the story with access to the entire National Pokedex (Minus a few Event-only Pokemon I'm missing) from the start. But I would first like to confirm: Can I withdraw my stored Pokemon from the bank if my game is reset? It seems that the only contributing factor is that I end up signed in with the same Nintendo Network ID, so as long as my network ID remains the same, I can withdraw stored Pokemon regardless of what save-game or cartridge is in my system, correct?
While I'm reasonably confident it works the way I think it does, past experience (My Pokemon Ranch being tied to specific trainer IDs, and something about the dream world being tied to the game's wireless settings) has made me just cautious enough to ask before attempting.