Does attending Stanford Summer Session improve my chances of being accepted at Stanford University?

Admission to Summer Session does not mean admission to Stanford University.

Stanford does not have a preference for students who attend Stanford-specific summer programs, including Summer Session. Overall, it is encouraged that you pursue any summer activity, class, or program, or work you are interested in. The fact that you are participating in a given program, activity, or work is not in and of itself the value-add to your application. What is important to Stanford—and, for that matter, many other colleges and universities--is how you learn, grow, and contribute because of these experiences.