Reading taterhead's advice prompts me to point out some differences that probably make my previous advice very bad:
When I went through boot camp in San Diego, I was the only MMNF in the company. We finished training on a Thursday, went to graduation on a Friday, then I left for Great Lakes for a week of self-paced propulsion plant basics and MM "A" school.
I was basically on my own until I arrived at NPS Orlando months later.
Now "A" school and NPS are in the same place, so it sounds like the Navy can group people together more easily.
So, you'll have to get input from a recent graduate. If they travelled as a group and did not receive their transfer packet (orders and service jacket) until arriving at Charleston, it sounds like it will not be possible. If you transfer during the week, you may not have enough travel and proceed time to make the trip. (Oh, they don't have RTC in Orlando anymore, do they? You'll probably only be allowed one day travel and proceed time, so if you don't go to RTC in Orlando, you won't be able to make it.)
This makes me want to delete my entire previous post. (In fact, I'm going to delete most of it right now if I can.) Where are you going to boot camp? If the only places for RTC are Great Lakes and San Diego, you definitely will not have enough time. Sorry to mislead you earlier, but as I said, my information is very dated. I wouldn't count on being a "special case", which would have to be a do-it-yourself transfer with a Personally Owned Vehicle. I would guess that's just not possible coming from boot camp because that type of travel would not be authorized.
Sorry, no. I would say that it is more a case of "not logistically possible" due to time constraints rather than "not allowed".