The DO organizations, of which the AOA is only one, on the ACGME board could easily join forces with say the IMG organizations to change policies that adversely affect non-LCME graduates.
Having a voice and a chair at the table does absolutely have an impact, if only to make concerns known. A lot of mishaps in roll out of new policies or marginalization of smaller groups of applicants/trainees is usually not intentional and often happens as a result of not even realizing how a new policy will affect others. In that case, even just having some representation makes a difference. The DO organizations literally had no say or input in the past and relied on groups reaching out to the ACGME to create MOUs and committees somewhat after the fact.
Now, there's nothing to say that the DO organizations will actually have the backs of DOs and DO students, but at least now they theoretically could when it comes to ACGME policies and changes.
It varies program to program what this means. For many it does mean extra required DO things, for others it's optional. This is why its important to ask each program what osteopathic recognition actually means there.