You would need a visa.
Technically you only need an M-1 visa for a full-time course (depending on the type, this is defined as 18 or 22 hours per week). If training is only incidental to your stay there and it's not a full time course then the situation is a bit dubious. In fact, if you apply for an M-1 visa knowing full well that you're not going for a full time course (as defined by the INS) you might actually be in breach of visa regulations.
Full discussion here:
http://www.pprune.org/forums/showthread.php?t=314913
Right now the safest option seems to be to obtain your M-1 in any case, since that's what everybody does and everybody (including the friendly INS official at the border) expects you to do.
I second Julians mention of the FAA CPL though. All you need for an FAA CPL is an ICAO PPL, but it doesn't have to be an FAA PPL. If you otherwise fulfill all the requirements (hours flown etc) and have the necessary skills and medical, it may be a very worthwhile investment and probably not much more expensive than obtaining an FAA PPL. I mean, you need to do a medical, theory exams and a flight test both for the standalone FAA PPL and for the FAA CPL anyway.
The worst thing you could do (but it looks like you already know this), is to get a piggyback FAA PPL and then add ratings to it. As IO540 said a while ago in another thread: you're then building a house of cards. The house of cards can be brought down by something very simple like getting a new JAA license with a new number issued for some reason. All of a sudden the foundation for your FAA PPL no longer exists and thus the ratings that you obtained on your FAA PPL vanish as well.