As long as you are BE with a plan to take the exam, I think you'll find few employers who will refuse you a job. The exceptions most likely would be jobs as a Department Chair, etc. however as a fresh grad, you probably won't be considered for those anyway.
Most of the problems with needing to be BC come from insurance companies refusing to reimburse for care provided by non-BC physicians. But for new grads, especially as a hospitalist this typically isn't a significant problem (more so when in private practice). You'll be salaried.