Would Pico de Gallo pair well with rotini and basil pesto

Wouldn't do it myself, but worse ideas have found their way onto some pretty expensive menus- maybe try it when you're eating alone, though.

No, I personally don't think so. The basil is the taste you want to predominate so I wouldn't have it compete with the pico de gallo, particularly if that includes jalapeños. I would and have serve pesto with a chopped salad of tomato, onion, and cucumber. Obviously it's up to you to make the call.