Why would you not be able to attend a Part 141 school?
I would say it is a whole lot easier to do your flying on a M1 visa with business on the side then doing your business on a B1/B2 and illegally training.
The school will get a slap on the wrist and the student is eligible for deportation with a visa violation.
Even here you will get answers from people who have done it that way or even claim it is legal but there are playing with fire.
Easy to say its Ok to go do it when you are not the one to be deported.
Despite all teh grey areas or percieved holes in the laws;
training towards the issuance of a license or rating requires the correct visa.
On Friday, April 12, 2002, the Department of Justice (DOJ) issued an Interim rule through the Federal Register (Vol. 67, No.71) proposing to amend 8 CFR Parts 214 and 248. This amendment requires a change of status from any non-immigrant visitor visa (B-1 or B-2) to a student visa (F-1 of M-1) prior to pursuing a course of study.