Hi Bethany,
When sending a batch email, it will only send once at the time you schedule it. It won't send any future casts unless you scheduled a recurring batch.
My understanding is it will evaluate the smart list criteria at the time you scheduled it to send. So if you set it up last night and 200 people qualified for your smart list and then you scheduled it to go out this morning, and in the interim another 10 people qualified for the smart list, I believe it will send to all 210 people who now qualify.
However if someone qualifies AFTER the send date, it won't send again.