When I bottle, I follow the typical step of boiling some water, adding bottling sugar, letting it cool, and adding it to the beer that's done fermenting (but still of course has live yeast floating around). Those little beasties probably would like a sip of O2 to grow better and carbonate the bottle better/faster, but I'm as careful not to add oxygen to the priming solution as I am to keep oxygen out of the beer. But I got to wondering, does anyone have any data or experience on aerating the priming solution? Seems like it would be an easy experiment that might have been tried, or maybe some author commented on it.
As far as I understand things, the yeast won't go through a serious growth phase in the bottle. The pressure and alcohol make for a harsh environment, and you shouldn't be using enough yeast to really consume any oxygen that you would add. At this point, you really want to avoid oxygenation, so that you limit oxidation flavors in the beer. Thus, you boil out the oxygen in your priming solution and prevent stirring air into the beer.
More oxygen might carbonate faster, but it would probably do so at the expense of cardboard flavored beer.