Sort of a strange question, I'm not sure how to answer. Just because a fellowship becomes "accredited" (usually this means by the ACGME/subspecialty society like SOAP, NOT the ABA) doesn't mean it will end with a board exam. There is no such exam for OB or regional fellowships, and cardiac doesn't have a "board" exam per se but rather an echo exam administered by an entirely separate entity (National Board of Echocardiography). To be fair the SCA is entertaining the idea of a board examination, but it will be a tough sell unless they can somehow pair up with the NBE so only one exam is needed.
The ABA administers subspecialty board exams for critical care, peds and pain (and apparently sleep medicine/palliative care). The Pediatric subspecialty exam was introduced in 2013 and people who had extensive clinical experience in peds are able to challenge the test until 2019 as long as they met certain criteria ("grandfathering").
That all makes sense, but unlike other subspecialties (like Raryn's endocrinology), you don't really need a subspecialty board to practice. It is entirely up to your hospital/group/whatever whether they will credential you for the work you are doing - for cardiac, there are many, many people out there in the community and even in academics who didn't complete a formal fellowship. But those days are changing and now for many community and certainly almost all academic jobs you'll need a fellowship. Chances are if you've done a lot of peds in your career just about all hospitals will allow you to continue that going forward, even without a fellowship in the distant past. But I don't really see how something like this would apply to OB or regional - these skill sets should be in any anesthesiologist's armamentarium, at least on a superficial level that would satisfy most L&D floors and outpatient surgery centers (perhaps not the esoteric academic center).
Last thought - the primary allure of a regional fellowship is for trainees to gain a little extra experience and typically they are paid as a part-time faculty member and take general OR call making 2-3x what typical residents/fellows make. The others who don't really fit into this category are probably looking for a way into academics. Helps bridge the gap looking for jobs or waiting on a loved one to finish school/training in a another field. With ACGME accreditation this will no longer be allowed so they'll be making what your critical care and cardiac fellows make... if I had to guess I'd say interest will plummet except at the highest level institutions for those interested in academics. I can't really speak to OB because I know literally nothing about such a fellowship.