Will getting rejected from a graduate school affect my relationships with the faculty members at that school?
I got hired as a postdoc at a university which had rejected my graduate application.

And not just that. When I started, I realized that they had made the right decision. The background level of the first-years was uniformly and substantially higher than what mine had been when I started. I would have gotten creamed.

You will have the opportunity to prove yourself in your first year. Do a good job, and any weaknesses in your application will be quickly forgotten.

Good luck!