It's a bit random! The application will either be accepted or denied once a member of the application team goes through them, and it's a bit hard to tell the exact time they're checked. I'd say it takes up to 24 hours to get a response!
As soon as you do your application, a member of the application team will have a look at your application, it should not take long to get a response to find out weather you were accepted or not. After you got accepted, you have to do an interview with a GP. If you pass the interview, you are in the NHS. It will take maximum 24 hours if not instant to get white-listed to play a NHS student. For what you can do as a student, you will be told at the end of your interview.