Well if you are a competitive applicant, then interviews usually come between August and November for Dec 1 acceptances. Some schools like Case start earlier than that, but they are an outlier with their interview dates.
i had everything submitted in time for the first mailing and received an interview at uconn on 6/30, i believe..so if you get your stuff in asap, you can get a few before september. good luck!
I hate to say it, but you may want to delay the studying abroad. If you're applying this year, a lot of interviews are held between September and November (i.e. all of my interviews were held during this time). If you were studying abroad, you would put yourself at a disadvantage because your interviews (might?) be rescheduled, but they would be rescheduled for after Christmas when the classes are already almost full.
interview rejections? no. they'll either send a rejection (before or after an interview) or, like most of the schools i applied to, they just have you wait forever until they eventually reject you or interview you.