It doesn't work that way. If they serve in a unit which was awarded the Presidential Unit Citation prior to their serving in that unit, they would wear the Presidential Unit Citation with their unit awards only while they are in that unit. If they serve in a unit when it is awarded the Presidential Unit Citation, then they wear that award at all times, regardless of what unit they're in.

However, if neither of these is applicable, then it may not be worn, whether the service member is a combat veteran or not.