When you link your bank account with Square, they have to send test deposits first to verify that it is indeed yours. These take up to 5 days, plus the time after that to actually transfer the overdrawn money.
Asking Square to take the money from another account would be no faster than moving it yourself to your primary one, because of this verification stage. Even if you had the foresight to link it ahead of time, Square only supports being associated with one account at a time.