Hi, ajnsylvie,
Yes, marriage in the U.S. is quite a bit less complicated than in Quebec, but it could present some difficulties at the border when your (then) husband re-enters Canada. If they feel he is an overstay risk - which could be compounded by your recent marriage, they could deny entry to him and create a very uncomfortable situation for both of you. Be aware of this possibility - from what I've read, it has happened to some people.
If you haven't guessed already, I'm a real advocate of the phrase, "the truth pays". I'd strongly advise against any plan of misdirecting the officers at the border, or of bringing him into Canada with the intent of having him overstay while your PR application goes through. It could lead to severe consequences.
If he is given a visitor's record when he enters Canada he can return to the border (remaining on the Canadian side) and have it extended, without paying a fee and without any trouble once your PR application has been submitted. I base this on my personal experiences during my own PR process. Be aware that the officers do need to see ongoing progress with regard to your case. Document everything (including mail receipts when you sent in the application, receipts of fees paid, etc) and have your (then) husband bring it along with him.
My wife and I were married in the U.S. because of the complexities here in Quebec and the fact that we had decided on a rather unusual venue for the wedding. We were absolutely honest about the wedding when we passed through the border back into Canada about 2 weeks afterward. We had no issues whatsoever, but it probably helped that I already had a long history of travel between the U.S. and Canada (100+ times over 4 years) and had passed over the border on many occasions with my wife in the 6 months before we were married. From my experience, the officers will work with you to help, so long as they believe that you are being 100% truthful.
I hope this helps - best of luck!