Well, it probably won't help you a bit and will look silly, so I wouldn't recommend it.
I'm not certain how recs for fraternities work, but for NPC sororities, you need a rec written from a member of that particular organization. If you were a woman going through NPC recruitment, your friend's sister could write you the letter or recommendation for Tri-Delt, but you'd still need to secure letters for each of the other chapters from members of those respective groups.
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I heart Gamma Phi Beta
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