I agree with SMRose. The deep understanding of the creative process which a stage manager can bring to the producer role can only be a benefit - as will all those other stage manager traits such as focus, passion, people skills, lateral thinking and accepting responsibility....etc, etc. I have made the transition to producing in the last few years. Even though I work in Australia and in the not for profit sector, I am positive you can make that shift yourself Josh, even if you are looking at a different producer model in a different cultural context.
However, I have just attended a theatre conference where some of Australia's most experienced Producers agreed (in a forum on creating the next generation of independent producers here) that successful producers are born not made and that it can't be taught in schools. Having been a stage manager doesn't guarantee success in the field. Find yourself a mentor. And build as many connections and relationships and networks as you can. They will all be used in your next career as a producer.
ChaCha