I would go ahead and apply. It's not going to hurt you and you could be offered an interview. Even if you don't get accepted right away, having your first interview under your belt is a good thing. I applied in the middle of my bridge program and had an interview. I didn't get accepted mind you, but I don't think it was because of that. I have known several people to be accepted on the condition that their BSN was complete by registration.
The following member says Thank You: