I am finishing an ACGME residency in internal medicine. I interviewed last year for AOA cardiology positions and ACGME positions this year. It is possible at least as of this year. You would have to take ACGME internal medicine boards as part of your requirements for graduating from an ACGME program, and if you choose to matriculate to a AOA fellowship, you will likely have to take the AOA medicine boards. It bascially comes down to making sure your intern year is approved (resolution 42, not a bid deal) for those applicable states and taking an extra licensure exam. Its not a big deal.
Applicants interested in this route will need to get resolution 42 approved, even if they don't plan on working in the 4 states (which is also where the majority of the AOA fellowships are located). It is one of the requirements to getting the residency approved. Then towards the end of residency, you petition the AOA to accept your residency as AOA equivalent. You must remain a AOA member in good standing.
And it's not just "taking an extra licensure exam"... It's a board certification exam. It makes studying for the usmle or comlex look easy (I've taken usmle, comlex, and ABIM medicine and ABIM sub specialty exams so I can compare). And the timing is off between ABIM IM exam and AOBIM IM exam by several months ... So it's not like usmle/comlex where you can take it around the same time.
However, if you pursue the ACGME IM and AOA fellowship, I don't think you have to take the ABIM IM exam. Last I checked, there is no ACGME/rrc requirement ... Your program may require you to take it, but I don't think it is an across the board requirement. For programs that do require their senior residents to sign up for the boards, they may view signing up for the AOBIM as fulfilling their requirement. If you don't have to take an extra board certification exam, and if you can save $1300 by not having to take ABIM, why sign up for it?
(An argument can be made that for medicine, ABIM is the gold standard when comparing DO vs MD, much more so than usmle/comlex, which in the eyes of employers and recruiting firms, are just mere licensing exams ... So by taking and passing ABIM it will tell people that your training is on par with your MD colleagues. Whether the exam itself actually reflects a competent physician .... That's another post/rant. And with the new MOC requirement by ABIM, you will only stay ABIM certified for 2 years before you are no longer certified and listed as "not maintaining maintenance of certification". Not sure it is worth it to do the MOC while still a busy cardiology fellow (plus you will have to worry about the AOA equivalent of MOC, which is OCC)