I'd say it depends on the school.
When I rushed, one out of five sororities had a house. Now, 3 sororities are housed, one has a suite in a dorm, and one is totally unhoused. Having vs. not having a house doesn't seem to have affected numbers, though this may be because all but one round of rush is held in function rooms in the student center - leveling the playing field.
It is absolutely possible to have a strong sisterhood without having a physical building to live in. I agree with WindyCityDZ there.
But PNMs sometimes have to make quick decisions about which groups to cut based on very little information. Round 1 parties can last as little as 20 minutes. If they've been shown beautiful house after beautiful house and are then taken to some classroom or function room, they may think WTF? and cut that sorority just for being unhoused.
I do hope this chapter succeeds, for obvious reasons
- but I'm concerned that, under these circumstances, being unhoused will hurt them.