I would try to take care of things at the ticket counter. Lots of countries and Mexico is one of them, do not have gate counters like we do in the US. All they do is make sure you have a ticket for that flight. As far as CUN goes, I can't really remember. But there are two terminal in CUN, the sked airline term and the charter term. Last time I was in CUN (July) Frontier operated into the charter term.
Just remember you experience will vary from what I have said and I have never had things work the same way twice in the Mexican cities.