well yes they can but it cannot happen without you setting it up. log in to your bank account to see if there is a transaction there.
Generally no unless you are using thier bill pay system.Just entering your bank account information does not put this into effect. The check register on Quickbooks is supposed to mimic what is happening with your real life bank account. The theory is if you pay a bill, you enter it into quickbooks as well, then you always have a track record and can see your available balance.