Mexican cheeses on otherwise Italian pizza
The short answer is yes, you can. We keep a wide variety of cheeses on hand. Quesadilla or Chihuahua Mexican cheeses are a great substitute for Mozzarella or Provolone cheese. The have a light flavor and work well with Italian foods. We always have these on hand, but they are not always easy to find in some areas. 

I often substitute simply because, while I might have the intended cheese on hand, there may be some that I need to use sooner than others depending on how long I've had them or how long they've been open. With mild cheeses, you don't have to worry about the flavor profile so much - it's more the melting. And the cheeses I mentioned melt well - just like Mozzarella or Provolone.

And to let you know, the reason I tried the other cheeses: I asked in a Mexican restaurant what kind of cheese they used and was told that it was "like American Mozzarella". So, I decided to experiment.

All said and done, all of these cheeses have a mild flavor and work in many dishes, regardless of the ethnicity. What you do want to stay away from are cheeses that don't melt well and are designed to keep their shape and texture under heat. One example would be quest fresco.