it depends also if you are a SNA or SNFO. SNFO they grant 10 days of BOQ time if you want. SNA they simply asked me if I wanted to stay in the BOQ or live off base. I stayed in the BOQ until I found a place...
however, if you elect to do what I did, bear in mind, you won't be reimbursed for the time you spent in the BOQ until you get to Primary. This is because API is considered an Intermediate activity on your orders (even though you will most likely be there for 6+ months).
No big deal though. This was my experience, it could be different for you. However, I have not heard of anyone being forced to stay at the BOQ in the recent past.