After I apply, I'm thinking of emailing many of the program Techstars mentors to get them interested in what I'm doing. Good idea?

Our mentors are dedicated to helping the companies that we select, but are not a part of the selection process. Emailing some or all of our mentors in order to try to influence them before being accepted into the program will hurt you more than it will help you (because they’ll complain about it to us). Our advice would be to focus on your application, which is what ultimately decides whether or not you are accepted to the program. We look forward to reviewing your application!