You can fly an FAA piggyback PPL on a medical that goes with the underlying "based on" licence (in this case a JAR-FCL medical) or on an FAA medical class III. So for your FAA piggyback PPL to be valid, you don't have to have a JAR-FCL medical per se, as long as you have an FAA medical.
I'm not sure about JAR without checking my old JAR licence, but certainly with an EASA licence the licence is only valid with a medical. So no EASA medical = no EASA valid licence = no valid FAA piggyback licence (as you need a valid foreign licence for the piggyback licence to be valid).