Some states only require a year of GME (e.g., your internship).
However, many hospitals now require that you be not only board-eligible, but board-certified as well before you can have priviledges at their hospital. It's expected that nearly all hospitals will require this in the future. Rumor has it that JCAHO (Joint Commission on Accreditation of Healthcare Organizations) is going to require it.
If you plan on practicing in a doc-in-the-box without admitting priviledges, then you can probably get by with it. I'm still not so sure it's a wise idea though. You would be better off to finish your residency.