No. In general, if the person is willing to violate the sabbath in public and even in front of a great rabbi, we assume he cannot count for a minyan. Rabbi Nachum Rabinovitch, (All Jews Are Responsible for One Another, from "Tradition and the Nontraditional Jew") based on the Rambam, says that chilul shabbos may not disqualify them if they are a tinok shenishba, but they have to accept the halachik requirements of a minyan to be counted for one. The Rambam said that the kaarites could not be counted for a Zimun because they rejected such halachos, so they cannot just be counted in for social reasons.