My daughter is a current DCP and attends a university that does not recognize the college program or accept DCP courses as credit (they don't accept AP courses for credit either but that's another story) so she had to apply for a special leave of absence that maintained her status as a full time student. I'm sure every school has a different policy for handling leaves of absence if they are not affiliated with or don't recognize the DCP but she handled her request by first going to her advisor to discuss the possibility of taking a leave of absence to participate in the DCP before she applied to the program. She also discussed the best time in her program for her to apply. In her case she only had a one semester window to participate or it would have thrown her degree program off kilter and added a year to her graduation timeline.
Her advisor outlined the procedure for taking a leave of absence, her school has very strict policies, and told her the approximate timeline for approval. Because part of the approval process includes mandatory written approval from her advisor she attained this in principal before she applied. She also kept her advisor updated throughout her application process so that she could pick up the forms and letter from her advisor as soon as she knew that she had been accepted into the program. My daughter also checked with the admissions department and housing to make sure she understood their procedures before she applied to the DCP.
On the day she was accepted into the DCP she emailed her advisor and picked everything up from her a couple of days later. She then applied for her official leave of absence. It was a bit complicated and she needed to stay on top of things with the different departments concerned because her request was a slightly out of the ordinary.
I hope that helps. As I said, I'm sure its different at every school but that's how my daughter handled the situation.