While I don't know much about NPC sororities and esp. on a big competitive school, I would *guess* that perhaps it would make it harder to compete (for lack of better term) with the other sororities with large beautiful houses.
*~However~* I think it could be looked at in a different way. If PNM's cut that sorority out JUST because they don't have a house, I would question what kind of PNM's that the other sororities are recieving if all they want is a beautiful mansion.
Maybe I'm just a very positive person, but I believe a true sisterhood can exist with or without a house. And I would hope PNM's can see that too.