Unfortunately, no, because he has no jurisdiction. The notary is granted the power to celebrate marriages thanks to the Civil Code of Quebec, which has scope only in Quebec. So even if you ask him/her to come and celebrate your wedding on a beautiful beach in the Caribbean, your wedding will not be recognized in Quebec.

You may, however, go see your notary in Quebec, get quietly married there in his/her office (with 2 witnesses who know you well), then go to Mexico and make a symbolic celebration with all your family there.

In any case, the requirements are sometimes so extreme in some countries to subsequently make your marriage recognized in Quebec that it is sometimes easier to proceed in this way …!