question, do you have any news reports etc that document that he counsled Cuomo? I would love to know if there is a direct connection. In terms of pro-abortion figures, there is indeed Kennedy and Kerry, Nancy Pelosi etc, but Cuomo seemed to have taken on a life of his own with the Notre Dame speech.
I don't know for sure whether Drinan ever directly counseled Mario Cuomo, although I imagine they traveled in similar circles. Mario Cuomo gave his famous speech at Notre Dame, so he was probably also influenced by the dissent that centered there, with Fr. Hesburgh, the leader of the Land o' Lakes movement that undermined and perhaps destroyed the Catholic colleges, and Fr. Richard McBrien, the dissenting heretic who was chairman of the Theology Department and a chief corrupter of the American Theological Association.
But Drinan was influential because he was one of the earliest to take this kind of position--not of outright dissent, but of speaking out of both sides of his mouth, staying in the Church while constantly undermining the teachings of the Church, most notably on contraception and abortion.
Drinan also demonstrated that it was possible to be a heretic but use doublespeak, and that the Church seemed reluctant to discipline such behavior.
Here's an article with some of the historical background:
http://www.catholiceducation.org/articles/politics/pg0020.html