I'm not sure it will carb any better going through the liquid "out", but I don't think it can hurt either. I would first purge the oxygen out of the keg using the gas "in", so that it's all gone before you start bubbling through the beer and stirring things up.
Primary #1: Umlaut my Kölsch VII #2: Empty
Secondary #1: Empty #2: Empty #3: Cab MerMarqeNac Wine
Kegged: Mugged a Monk Paters
Bottles: Dark Belgian Strong, Black Raspberry Rhubarb wine, RIS, Carmel Apple Cider, Big 50 Barleywine, Framboise Lambic, Barolo Wine, Berry Rhubarb Wine, Black Currant wine
On Deck: BGSA