Unlikely you will end up in the Pen for instructing on your FAA PPL but you will certainly get it suspended. Also you are inviting the appropriate people to look at your visa status. Some schools do it all by the book, some are just straight bent.Unfortunately no middle ground and being CAA/JAA approved means nothing.
Regarding FAA licences, I heard Soloflight at Humberside just got approval for FAA written tests.