Basically, the short answer is, "it depends." The long answer is a bit more complicated. I really didn't get any time off between BMQ and SQ. I graduated on the 23rd of July from St. Jean, and my SQ started on the 31st of July in Gagetown, so I was in holding for about a week, just sitting on my hands for the most part, unless the MCpl gave us some minor task to do (take out the garbage, move furniture, etc...). THAT SAID, the guys that came from Wainwright had about a month on PAT prior to jumping on our SQ course, and they were granted the opportunity to take leave.
So in summary, again, it depends. You probably won't find out until the end of your BMQ course though, so I wouldn't make plans.