Short version: yes, but almost certainly less than you fear, and in a more mechanical way than you think.
Every chapter has a minimum GPA requirement, set by their national organization and sometimes raised by the campus chapter, commonly landing between 2.5 and 3.0. Below a chapter's minimum, they usually cannot invite you back regardless of how great your conversations were, it's policy, not preference. This is the actual way GPA affects recruitment: as a floor, not a ranking.
Above the floor, GPA mostly stops mattering in the room. Members are not comparing a 3.4 to a 3.7 in selection meetings, they're comparing conversations. Chapters do care about their overall GPA (it affects their standing with the university), so a strong GPA is a quiet plus, but nobody gets picked for it.
Incoming freshmen: your high school GPA is what counts, and requirements are typically applied the same way. If yours is under about 3.0, look up (or ask your Panhellenic for) chapter minimums before the week so you know your realistic map rather than being blindsided by a schedule.
Current students: your college GPA governs, and one rough semester can bite harder than people expect. If you're near a cutoff, ask your Panhellenic how minimums are applied, some chapters evaluate case by case.
If your GPA is genuinely low: you have options. Some chapters have lower minimums than others. COB after formal recruitment sometimes has more flexibility. And rushing a year later with improved grades is a real path plenty of women take. A number can close some doors, it has never closed all of them.