I'm reading Sciencewoman's post as, similar to schools in San Diego, that "silence" is in place from the beginning of the year but recruitment doesn't begin until a week or two into the semester/quarter. During that time other student organizations, including non NPC sororities are actively recruiting membership.
To the original question, since the NPC rule is an agreement among NPC groups only I don't see why it would be grounds for immediate disqualification from membership. It doesn't mean that individual women, either the ones selecting the colony or the chosen members, would not have a huge issue with it. So, yes, it could hurt your chances at membership and yes it could cause you trouble even if you do get selected to receive a bid.
As for the idea that NPC should apply the no dual membership rule to all groups outside of NPC, I think that would require a new NPC UA. The current one, to the best of my understanding, was created to stop member organizations from cannibalizing each other. If NPHC wants to enter into some UAs with NPC then I think that could work. Since NPHC itself has no, or few, UAs I don't see that happening any time soon.
**Post written before I finished my morning coffee. I apologize if anything doesn't make sense.
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