Warming them up once they're carbed will force some of the CO2 out of solution, so it will take a little bit once you move them to the serving chamber to get them to recarb again. It will certainly work though, and should condition faster at room temp. You could always carb at room temp too, although it would take higher pressures, which I suppose for a sanke would be tougher to get rid of than in a corny with a pressure relief. The other option is to forgo force carbing and just naturally carb in the keg. You've got to use less priming sugar than for a batch of bottles (you'll have to search for the proper amount), but add it to your keg and let it carb up naturally at room temp until its carbed, then you can move it into the kegerator.
There's a lot of debate on the benefits of naturally carbing, but the one thing that it would probably help the best in your situation is to remove some of the oxygen that inevitably gets into the keg during transfer. Since at room temp oxidation should occur faster, the second fermentation will help to prevent that while the keg sits at room temp. The downside to naturally carbing is if you've got a big beer that you want to serve quickly, but might not be carbed up in time. Although, while I've heard that big bottled beers take longer to carb, I'm not sure if the same happens within a keg, so you might be alright.