You should review FAR 61.65 regarding training towards an FAA IR.
Whether you choose to use the non approved Flight School is your call . You are at least aware.
This other recent thread on the subject of legalities points out what can happen.
http://www.pprune.org/professional-p...ml#post6941529
Will you have access to a N reg when back in Europe in order to exercise the FAA IR? (until EASA change the regs for Euro residents).