Probably a better question is whether you can quickly access your pistol while carrying all of your bow hunting gear ...
While it happens very rarely, if you watch the videos of guys getting charged, the amount of time between "oh, I'm getting charged" and the arrival of fast moving swine is a pretty short interval. It's also worth noting that 9 times out of 10, a "charge" is merely a scared pig running to a spot where you happen to be. Of course, time number ten things get pretty interesting.
This video, posted by another member here, is probably the only one that I've ever seen when there was a significant gap between the moment of realization and the moment of truth. Even here, look how touch and go it was: