It is possible. Some styles will carb faster than others. However there is a difference between appearing carbed and being carbed. For example I brewed and american wheat not too long ago that was carbed like crazy after a week. However it was all head, no real carb after the pour. So it appeared carbed at first but had no lasting power.
Assuming that somehow you have the appropriate head, head retention, and sufficient bubbles after the fact, I'd still leave it for a few weeks. Taste one every week and note the drastic improvement in flavor. It's not all about carbing when you bottle condition, a lot of the wait time is for the yeast to clean up and dramatically improve the taste!
That being said my first brew was an APA, and it was so good after about 10 days that I drank the hell out of them. It wasn't till the last couple that I realized how great it was after waiting a while.