No, far from it. Our Synod of Bishops had submitted a proposed charter revision in 2000 or so, which was characterized as "semi-autonomos," but the Ecumenical Patriarchate rejected it. There was a battle among the laity, (and priests, too), over this matter, but the latest charter ("granted" in 2003) maintains tight control by the Patriarchate of the Holy Archdiocese of America, though progressively, it did recognize our bishops, who were elevated to metropolitans, as a provincial or Eparchial Synod, as the "instrument of governance." Despite some compromise language in the charter about advice from the American Holy Synod, the right to elect the Archbishop of America is the "exclusive" prerogative of the Patriarchate. Two years ago, the Synod submitted a proposed list to the Patriarchate of future candidates for the Archepiscopal Throne, which was rejected. Another example, all resolutions of the Bi-Annual Clergy-Laity Congress, the supreme "legislative" instrument, must be approved by the Patriarchate, prior to implementation.
In practicality, historically, the Patriarchate has allowed independent governance of its Eparchy in the Western Hemisphere, except for a few notable exceptions; our beloved Patriarch Athenagoras, of Blessed Memory, had essentially vetoed the 1970 resolutions, for a new charter requesting some level of autonomy, and for the use of the English language, as needed, in the Divine Services, although, in practice, the Archdiocese did move toward the practice of "flexible bilingualism," anyway. Patriarch Bartholomew has been a comparatively aggressive administrator of the Archdiocese of America, especially during the last two years of Archbishop Iakovos' archepiscopal tenure; he is believed to have forced +Iakovos' retirement. The Patriarch also exercised quite amount of influence during Archbishop Spyridon's tumultuous 3 year tenure, '96-'99. Both the Synod of Bishops and the Executive officers of the Archdiocesan Council were called to the Phanar for conferences more than a few times. In the late Summer of 1998, the Patriarch halted a planned meeting of the newly appointed Archdiocesan Council, because "the friends of the Patriarchate," were not included in the appointments, according to the authorized memoir of Archbishop Spyridon. Except for the charter debate earlier in this decade, the Patriarchate has not involved itself in the internal affairs of the Archdiocese, but controversial issues have not been debated of late, either.
Note also, the Archdiocese of America covers the United States (and the Bahamas) only since the day of Archbishop Iakovos' retirement on his 85 birthday, July 30, 1996. There were initiated on that day distinct metropolis' for Canada, Central America, and South America.
One of the problems that have enabled this strong administrative posture by the Patriarchate, is not completely attributable to the Patriarchate. There is an influential priest, a friend of the Patriarch's, referred to by Orthodox Christian Laity (OCL), as the "Patriarchal Nuncio," who leaks regularly, also according to Archbishop Spyridon's memoir; and commonly believed by most observers. Some of the metropolitans, too, maintain relationships with the Patriarchate, and communicate their concerns; however this practice was more prevalent in the last decade than it is currently.