yes, yes, yes, it is possible.
I have a sociology degree and only happened into theatre. I have worked in theatre 6 years since graduating undergrad, the majority of which was not even in stage management.
I would say call up the programs you are interested in. Send them your resume. Chat. See if you think you'd be a good fit. Definitely apply. As Emily says, they might not take you immediately but you should try.
I'm also at Rutgers. Very few people I know here have undergrad degrees in theatre.