If housing is assigned to him as a single person he will not be entitled to BAH.
That said, if he wants to go it on his own dime there is nothing stopping him.
Disclaimer #2: There was a time when barracks had to be 9X% full before commands would allow personnel who desired to move out of said barracks to request same. If the request was granted then said sailor would get BAH at the single rate. Usually this was done on a seniority basis. The reason they'd let people opt out or move out was they needed the 5% give or take for transient or temporarily assigned personnel.
Things may have changed so don't quote me on the latter.
Caution: I have two brain cells. Don't expect me to use them both at once.