is one (or more) port(s) connected to equipement that is on another power system? Ground differential could then cause nasty issues....
Normally not, because the ethernet ports are isolated by little transformers that are spec'ed to allow a few kV of voltage differential between the equipment.
Of course this is different when shielded cable is used and the shield is connected at both ends, and also for other ports (serial, USB).
However, even when the entire unit is not at ground potential and is powered by the original supply, the isolation between mains and output in that supply should still protect it against voltage differentials in typical operation. It should also withstand more than a kV.
That is why I mention untypical voltages, like nearby lightning strikes. That can cause voltages that destroy everything.