I think not. I think Catelyn was right, that Stannis wanted to parade Edric in front of the lords of the realm to show that Robert’s children looked like Robert and Cersei’s children don’t.
As King, I don’t know what Stannis would do about the landholding question. Robert choosing to divide up King’s Landing, Dragonstone, and Storm’s End among the brothers was a particular idiosyncratic decision, and Stannis might well be more the type to hang onto them himself, or parcel them out to his children.