I will start off by saying I first had to look into what a pressure barrel actually is. Looks pretty sweet! But yeah, if you are using priming sugar, I agree with m00ps. Very good point about the headspace in the vessel. However, there are a few more variables to consider:
What style of beer you are priming.
Amount of priming sugar used (this ties in with the style of beer, but can get kind of "sciency")
And the viability of the yeast cells remaining in the beer.
(of course, these may be overcomplicating the answer if you just want bubbles.)
I have switched over to kegging entirely, so it's been awhile since my last endeavor with priming sugar, but I'd say to not give it less than 10 days before cracking one open. I used to wait 3 weeks when priming just to ensure I wasn't wasting anything.
The best part: it's still technically drinkable! As long as you don't mind the beer being a a little undercarbed (and a touch sweeter than it's fully carbed twin), cheers!