I am basically going to tell my internship the truth (i.e. if I got official acceptance for the EAPSI there's no way I would turn it down). They can wait for two weeks if they really like me, or they can look for other candidates. I had already asked for a 10 day extension on their original deadline, so I feel kind of guilty stringing them along any longer knowing that I will turn them down if I get the EAPSI.
But from what it seems like, once you get tentatively accepted, it is extremely likely that you will get officially excepted. It is nice to have the internship as a backup though...