Thanks everyone for offering your advice. You all raised several issues that hadn't even occurred to me, and I appreciate the additional perspectives. I haven't quite decided how to proceed, but I am definitely keeping everything you all have said in mind. I'm sure this stuff won't matter to me as much when I move away for law school in a couple months, but for now, I'm working an unchallenging summer job in the next town over from my college, and I guess it's hard to keep my nose out of the chapter's business.
I did want to take the opportunity to respond to some of the issues raised in the preceding posts. First, the sorority in question is only "struggling" in the sense that they're also considered "lower tier" on our campus. However, they made quota every year that I was at the school. They seem to have a bit of a problem with attrition post-Bid Day, though, from what I understand. The reason I referred to them as a "competitor" sorority is because we pref most of the same pnms, and they seem to do the most "talking" about us during recruitment. While they are not known as one of the more desirable sororities on my campus, they don't suffer from the same negative reputation that we've somehow acquired, as far as I know. Anyway, I don't think they ever have a problem filling their house, because every sorority at my school has significantly more members than they could ever board in their houses at one time (mine included). I know our chapter house has a rule that you must be an initiated member to live in it, and I don't know if they have the same rule we do, but, again, I highly doubt that they have a need to fill their house.
As far as our campus Panhellenic climate...our campus has a very established Greek system. We do have a dedicated dean of Greek Life who is an alum of a GLO, and most "dirty plays" by the Panhellenic sororities are done with full knowledge of the rules that are being broken in the process. However, during rush, the Panhellenic officer in charge of recruitment and her team are pretty much given full authority. Dirty rushing is rampant on my campus, and though there are stiff penalties in place for it, it seems that reports are rarely followed up on. I'm not really sure if the dean would take action on this, and obviously, if I tell our membership chair, it would be up to her to decide if this is worth pursuing. I just wanted to make sure I wouldn't be overstepping any boundaries by bringing this to her attention as a recent alumna. Though it's really impossible for me to verify if this girl has actually pledged the other sorority or not, the membership chair would clearly be in a better position to do so, and of course no one from my chapter would ever bring this to the greek life office without strong evidence that the situation had occurred.
Again, thanks for all of your help, and if anyone has anything else to add, I'm sure I'll be checking in on Greekchat periodically as I while away the hours at my job.