Will I have a chance at being successful in the Musical Theatre business?

Nobody can give you a definitive answer. Some amazingly talented people struggle for years upon years to achieve success, while some less talented actors will get lucky and become stars. Luck is as much a part of it as talent and dedication. It also depends on what you definition of success is. Chances are you will work other jobs to supplement your income for quite a while. I've heard many professionals say to young people interested in pursuing a career in theatre, "If you can imagine yourself happy doing anything else, do it." It's a tough business, but it you're truly dedicated, you won't take "no" for an answer.

On a side note, you can have a career in the theatre beyond being a performer in musicals. There's a whole world of straight plays you're ignoring, and you could also be a writer, director, designer, stage manager, etc.