Idon't think entering under the VWP will work *if* you wish to obtain an FAA PPL, CPL, Multi, IR or type rating because you still have to pass the TSA's insecurity clearance. I could be wrong but that's my understanding.
I don't think all is lost though. I seem to recall that though only a 141 school can get SEVIS approval you don't necessarily have to do their 141 course ie it might still be possible to train under that school's Part 61 program.
I now manage a 135 certificate that's a sister organisation to a 141 SEVIS approved school. I'll ask at work tomorrow.