From my understanding, when you give two weeks notice and state that your last date will be ##/##/####, this date will be considered your employment termination date. It is the employer's discretion whether they will send you packing the your turn in your resignation letter or let you work the remaining two weeks. If they kick you out the door that day, I'm pretty sure it is the industry standard to pay you for the remaining two weeks. I know that is my company's policy.
I would take a bet that if you last day stated in your letter is after your 1-year period, they won't ask for repayment of the bonus. Depending on your relationship with your boss or whoever controls salaries and bonuses and how ethical they are, they might demand it back, withhold your last paycheck or 401K, or just give you hell for leaving. But I don't think they have any legal justification.