No, those agencies currently have no power over COCA or DO schools in general. And until the final details are worked out, residencies and the match system will also remain totally separate.
My speculation is merely that it seems inevitable in the next few decades that with the merger of residency's under ACGME, the oversight of medical education will also be a place of potential merger that will be explored. And frankly, it is probably for the better for all parties involved, even if distinctions like OMM training never totally overlap/unify. The structure for the proposed GME merger is that the AOA/AACOM will be like "subclusters" within ACGME and I think that COCA would probably be the same thing under the LCME.
If I were you I wouldn't be worried about it. Depending on where you are the process it could even benefit you. I can only pray that my class will receive the GREAT benefit of a single match.
Yes though, with the residency mergers if/when certain AOA-accredited residencies don't meet the uniform standards they would go through the same process that all current ACGME programs do, which in my understanding is probation and if uncorrected, closure. Unless the AOA program couldn't feasibly make the improvements in which case yeah it would close and the money would be reallocated to another potential existing or expanding program for their slots.