On Pokemon X and Y, I plan on re-setting my game. If I were to put all of my Pokemon into the bank, then reset, could I re-link the bank and the game so I can re-obtain my Pokemon?
Yes, you can deposit your Pokemon in the Bank, restart the game, and withdraw them again. You can even insert a different Pokemon cartridge and access your Banked Pokemon on the new cartridge as well.
Do note that you cannot keep items this way - items will be returned to your backpack upon depositing Pokemon in the Bank.