Since you are starting on the 13th, chances are that your pay (if you were not a BDCP candidate) will not take effect on the 15th pay date. This is because the cut off for all pay matters to take effect for the 15th pay date will be (normally) between the 6 - 9th. My guess is that you will not receive your first pay from the Navy until the 1st, at which point said pay will be retroactive to the 13th. So, you'll receive about 17 days worth of pay on the 1st.
The Pay and Support Detachment (PSD) up in Newport have been doing this a long time and seems to be pretty good. I haven't heard any bad things about them concerning pay issues, so I won't worry about it too much.
Plus your class Chief will do everything he/she can to prevent their students from having pay problems at OCS... Navy Chiefs are bull dogs with that kind of stuff... being a PS dealing with Navy pay as an enlisted, I know that all to well!