Carb level effect time required?

This may seem like a dumb question but I need to ask anyway. Does the carbonation volume effect how long it takes to carb up? The obvious answer to me seems to be yes but I know in brewing the obvious answer isn't always the right answer. The reason I got to thinking this was that I kegged a bitter last week and primed it with .4 oz of sugar as per an online calculator. Within 4 days it had enough pressure to pour out with some foam and have a nice mouth feel to it. I realize that I will still need to cold crash it so the beer can absorb the co2. Any thoughts? Should I go ahead and cold crash it after a week?

To get the CO2 to go into solution you will need to crash it. Pulling a beer from it early is going to deplete some of that carbonation before it has a chance to go into solution. How big is the keg? 0.4oz doesn't sound like a whole lot, even for a keg, unless that is oz per gallon or it's a really small keg.

I used this calculator
http://www.tastybrew.com/calculators/priming.html

and its for 5 gallons, I selected, special/best bitter which suggested about 1.025 volumes. Normally I half it for kegging but I figured the difference in .4 and .2 was negligible.

Okay, that makes sense. The beer will have about 1 volume in it at the end of fermentation if the temperature is near 60 degrees. It sounds like you are going for an English cask conditioned level of carbonation. I was thinking 2 volumes like a standard ale or lager.