A master's in CS couldn't hurt...
On the other hand, are you sure you're adequately prepared to do graduate level work in CS? In other words, do you feel like you have an adequate knowledge of fundamental CS concepts? Just because the department is accepting non-major students doesn't mean they guarantee you will succeed.
There are ways in which you can assess your readiness. Try the CS GRE subject test online. Read up on the course descriptions relevant to the CS major.
As far as your question goes, though, if you get into CS there's no guarantee that you'll get a job involving anything you did in undergrad. Chances are good, but... anyway. Does this answer your question, or were you looking for something more?