Yes, they do it. We use it as much as we need it. You can do it even hours before the flight giventh you purchased it less than 24 hours before.

Even more, last time I checked, weekends did not count, so If you purchase on friday 2pm, you had until monday 1:59 to cancel. This may have changed.

Also, a year back, the only exception was Airtran that only allowed 4 hours.

LR