If the training you are going to be undertaking will lead towards a licence, be it an FAA or other such as JAA, then my belief is that you will most definately require a Visa.
In order to obtain, say an M-1 visa you will require a flight school who are approved to send out I20M forms, these forms are required to apply to the US Embassy for your visa, without one the US Embassy will not issue an M-1 visa.
IIRC a BFR doesn't count as training towards a licence as you already have the licence, you are just revalidating it.