There should be no issue with a PE being connected to the core via another PE.
The basic difference between a P and PE router is mostlty academic. In principle, a P router only does label swapping, whereas the PE does label imposition and disposition (or if you prefer, label pushing and popping).
I have seen some core routers from other vendors only being label swapping capable (P only) but I have never seen a device supporting MPLS and not being able to support label swapping (P functionality).
Hope this helps,
Regards,
Harold Ritter, CCIE #4168 (EI, SP)