An overdraft is no problem. As long as you have not been made bankrupt, defaulted on loans etc.
The thing about FSA application is to be as honest as possible and declare all your defaults, loan arrangements etc.
I have been FSA registered many times, including when I have had overdrafts.
I also know of people who have had ccj's, declared the fact to the FSA, got their employer to clear the debt, and then FSA agreed approval / registration.
Just be honest with your application. If you don't declare everything on your application, FSA will do a background check, and if they find anything you haven't admitted to, you will not be registered because you are a dishonest person.