Depends on the particular state. In TX, for example, you can take it at the masters level, and if you score high enough, carry that over to psychologist licensing once other criteria are met.
Yes, some states allow for taking the EPPP at the master's level (Texas and Kansas I know for sure do), and some states will let you take it during internship if they don't require post-doc hours for licensure. Someone from my internship cohort was able to do it by applying for licensure in Alabama.