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: Big 50 Barleywine #2:Empty
Secondary #1: Peach Rhubarb Wine #2: Empty #3: Empty #4: Framboise Lambic
Kegged: Orange EPA, Piker Liker Porter
Bottles: Red Rye IPA, Dark Belgian Strong, Belgian Golden Strong, Kicked by a Moose Scotch Ale, Apfelwein, Russian Imperial Stout, Carmelite Tripel, Rhubarb Wine, Barolo Wine
On Deck: Umlaut my Kölsch V