I think that for many of the international students, the consultants (particularly in Asia) have relationships with AOs and that often, their input is helpful to the AOs because they know more about the middle schools, competitions, etc. I seriously doubt though that an AO would admit a kid based on a consultant’s recommendation. Over time, the consultant’s input will prove reliable (or not!)
I knew 2 very well established consultants in the U.S. and my overall impression is that what they did best was find the right fit – picking schools where the student would thrive and compile a list that ensured there would be good choices come M10. (Not, as @cityran experienced, 100% acceptances.) At some level, if they do this right, no advocacy is needed although both of these folks I know seemed to know EVERYONE in admissions and was highly respected. So if one of these consultants called the AO to chat about xyz’s interest in abc , the school also knew that this kid’s fit for the school had been vetted.
I would be somewhat wary of a consultant who offered tiered services like this. They are essentially saying “I’ll help you put together the best list and application possible but I’ll be telling the schools to admit the ones who paid me more.” Feels all wrong.