It might. If you get an early interview at a school you want to go to, then accepted, then you don need to go to anymore. If you aren't so lucky, you might have some during that time. Most schools will let you reschedule to a different time if you have a good reason.
Unless you are near the end of interview season...thus they can't move you back in the schedule any further.
In any case, I think the greater worry is that you get important notifications during that period that are time-sensitive. Hopefully, you've made arrangements to get that handled....like having your mail go to your parents who open it for you and tell you if you have something important.