You have to get an I-20 from the school first.
This answer is of a general nature and should not be relied upon as final, nor is it intended as legal advice. Consult with a qualified attorney before making any legal decisions. Gen Kimura, (832) 247-6932.
I would speak to an attorney first. I foresee some intent issues. And my colleague is correct that before obtaining a student visa, you have to be accepted into the school and have Form I-120.
This is not legal advice and a client attorney relationship is not created. For a free consultation call (718)234-5588.
DON'T DO IT.
Your plan is full of potential heartaches.
1. The process of COS from B to F takes 4-6, or more, months.
2. If you file for F w/in 90 days of arriving ... immigration can accuse you of having 'deceived' the border guard when you came in and declared yourself to be a tourist.
Get an I-20 and go to the US Consul to get the proper F visa.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship.