Well, it depends on what you mean by "hurt."
Will they hold it against you? No.
Will it reduce your chances of acceptance? Maybe.
With rolling admissions, it's always best to get everything done early. If you go to the first interview, they may have 20 interviews for 100 seats available and they will be more relaxed about quality at that moment; if you go to the last, they may have 20 attendees for only 10 seats left (large exaggeration, but it's to make a point), so they'll be more tough because they want the best applicants to fill this seats.
Does that make sense?
Considering the last interview you have to choose from is in October, which is still very early, there probably won't be much difference. However, I believe the principle I mentioned above still holds true.
I hope that answered your question and good luck on your interview!
