HIGHLY doubt it! It's the number of overnighting jets that determines what city's "domicile worthy" at SW. I'm not sure what they got in EWR nowadays, but I know that between AAI & SWA in LGA there can't be anymore than eight RONs. Not nearly enough for a domicile.
However, a EWR/LGA codomicile would seem feasible. Perhaps not how but in the future with a little more growth? NYC is the biggest air travel market in the world. I can't see SWA not wanting to get in there in a big, big way.