Reservist BAH during Basic/OCS

I just read on this subreddit that I can get BAH during basic with no dependents as long as I have a lease. I currently live with one of my parents in a city with a low BAH. However, my other parent lives in a city with a high BAH. Can I show up to BCT/OCS with a lease from them so I can get more $$$? It’s almost double per month.