Theoretically speaking they probably can have some Union stations and some non-union stations.
Let's take a look at retail for a minute. Stop and Shop has some union stores and others that are not. I think in CT, Mass, and RI they are union and I think in NJ and NY they aren't. And they have two different divisions of Giant one based in PA and one based in MD which has locations in MD, DC, DE, and VA. One division is Union and the other division is not.
Shaw's too. When Shaw's was in CT they were a Union Shop. In Maine they are not. I can't speak for Mass, RI, VT or, NH. Their Philly-area sister chain ACME is Union.
Now Shoprite which is a NJ based co-op grocery chain where most of the 220+ stores are independently owned and operated so it's up to each owner whether or not they are union. They are about 20 (or so stores) that are not independently owned and operated and are owned by parent company Wakerfern.