This is an interesting question and the short answer, to the best of my knowledge, is "no." Similar to residency training requirements, your training must be in the US for you to become ABOG board certified in the sub-specialty of your choosing. More specifically, you must have completed 32 of 36 weeks of fellowship training in an ABOG approved program before being given permission to apply for sub-specialty board certification examination(s).
To that end, you must understand that there is a difference between "board certification" in a sub-specialty and "practicing" various aspects of a sub-specialty. For example, as an MFM, my job predominantly entails prenatal diagnosis (ultrasound, diagnostic testing). Although most folks are MFM fellowship trained practitioners, there are some that perform prenatal diagnosis by the virtue of having done a 1 year radiology fellowship + genetics fellowship OR grand-fathered into the field before board certification was available OR are an OB/GYN that managed to land the privileges from the hospital to do it. In this scenario, I'd assume that you could go outside the country, get trained, and then return to the states in hopes of getting privileges to do what the sub-specialist does without the ABOG board certification or fellowship training behind your name. I don't personally know how feasible this option is as I haven't seen it too often, but I'd strongly recommend researching it out before taking this route. You might be limiting your practice area as many employers will likely look at fellowship trained and/or board certified sub-specialists instead.
I hope this rambling post helps 🙂
Best of luck!