Nope. Don Adams is the president and the office of the president is an administrative role. Don Adams is not anointed, and only anointed ones may be on the Governing Body.
Nathan Knorr was the last real president that made "spiritual" decisions. In the mid-70s, a few years before Nathan Knorr's death, The Governing Body started to "govern" in terms of spiritual matters. After that Fred Franz, then Milton Henschel were the president's and on the Governing Body. However in 2000 all the Governing Body members resigned from their executive positions in order to concentrate on spiritual matters. At that time Don Adams became the Watchtower president.