I had a lengthy conversation about this with an agent last week. He knew the answers with confidence, so I think he knew what he was talking about. He said that if I canceled an award, he would process the money right away and it should be refunded within a day or two.
He then said that normally the miles would be redeposited within 15 days. But that he could send an email to the department and ask them to redeposit, but that it would be about 3-5 days rather than 15. He said there was no chance of a same day redeposit.