Can you receive BAH for taking more than 15 days of leave?

You received transient BAH. It is something that you are authorized during PCS.

Someone made a mistake. You should not have received BAH. You are single, live in the barracks and have no dependents. You taking leave has zero bearing on BAH at all. It is literally you taking a vacation. There is no training, you are not in school. You are taking time away from your job for personal time.

I would enjoy the extra money but honestly the Murphy and the military have a love affair, would look for the bean counters to find that error and you to get clocked for it at some future date on your LES.