There are almost no MSN programs that prepare people for a career in Nursing Professional Development (the official name of the certified specialty in "staff development"). So ... lots of people get MSN's in nursing education and then teach in hospitals. It's common.
I do suggest that you supplement your MSN with continuing education programs that focus on staff development issues to help you adapt your educational knowledge to the different setting, type of student, and type of education provided by hospitals. As I think you recognize, there are some real differences in the type of education provided by schools and the type of education provided by hospitals.
You might also join NNSDO and start reading their journal regularly. (The Journal for Nurses in Staff Development) Also, check out the Scope and Standards of Practice for Nurses in Nursing Professional Development (available through ANA and /or ANCC). That will give you a feel for the field and what you will need to focus on in hospital education.
Good luck to you.