So I never got a response, just thought I'd follow up in case anyone comes across this thread in the future. I went ahead and barreled 2 liters of the vanilla imperial stout, left it in there for a week, then bottled, and left in the bottle for 2 weeks to carbonate. I only got about 5 beers our of the barrel, with another 1/2 bottle leftover.
Maybe the stout hides the oak flavor better than some other brews, but leaving it in there for a week did not dramatically alter the flavor to a more oaky variety as much as I would have hoped. There is a note of the flavor in the after taste, but it is greatly overpowered by the high ABV of the stout. My advise to anyone attempting anything similar is leave it in for a week at the least, try for 1 1/2 to 2, and rotate the barrel every couple days to maximize oakyness, otherwise it just doesn't quite feel worth it.