The transfer desks have a "general side" with service agents and a side with more experienced ticketing agents on duty. For a day of departure upgrade I believe you need to go to the ticketing side.
There is no time limit as long as it`s on the same day.
According to my source they will first check how many seats are available in the cabin (= actual seats in configuration minus seats sold, this is not = to not the number of seats for sale which can be higher due to overbooking factors) and subtract waitlist business class passengers.
And of course they check if you have sufficient miles and if you need to pay a bump-up fee to B-fare class.
Note that V-class tickets are not eligible for the fare bump-up so they cannot be upgraded at all.