Not sure if I’ve seen this answered anywhere, but my gut says not to count on it. Those timers are usually hard-coded. Currently there are no transfers at all for Classic as they’re temporarily closed for the upcoming launch of BC.
The only real way for us to check as players is to look at our Transaction History and look for the transfer and the date it took place. I don’t think it shows the specifics for which character you transferred, but it should give you an idea of the date at least 