BDCP stands for Baccalaureate Degree Completion Program. Basically, if you go to a school with NROTC, the Navy will contract you, pay a certain amount of your school costs (it's a fixed ceiling, not a percentage), and then you go to OCS and are commissioned afterward. If you decide not to commission, you carried an obligation to enlist, if I remember correctly.
Anyhow, doing sports isn't going to hurt your chances of getting into BDCP. The worst thing that could happen is that the Navy won't give you more money than you need to pay for tuition (that is, if they're willing to pay $10,000 a year and you only need $3,000, they probably won't let you pocket $7,000). In the end, you'll still have school paid for and you'll still be a commissioned officer in the Navy.
Be aware that there aren't many slots open in the unrestricted line right now. SWO is *very* hard to get, and NA/NFO are always tough to get. They're pushing a lot of people toward Intel, Supply, and Nukes, or at least that's what I've been hearing.