If a person converted into the Reform or Conservative (Masorti) Movements, would Orthodox Jews consider them to be Jewish in the first place?
This is also assuming the person keeps basic Kosher (not eating Treif foods or Milk/Meat together), is circumcised (if male), and went through study, a Bet Dein, and Mikvah.
Could this person (if male) be counted in an Orthodox Minyan as well?
The issue here is essentially one of lowest common denominator. A conversion will only be accepted by Group X if they think that Group Y, who oversaw the conversion, did so appropriately and successfully, following all the relevant laws as understood by Group X. Otherwise, Group X will continue to view the potential convert as a gentile with all that entails.
As it happens, most if not all Orthodox rabbis will find a problem with some element of a Conservative or Reform conversion, often in the eligibility of the members of the Beit Din or in the acceptance of "all" of the Mitzvot (as taken from the Orthodox perspective). Rav Moshe Feinstein assumes as much in his Igrot Moshe EH 3:4.
For any actual case you should take all the details of the conversion process and speak to your local Orthodox rabbi.
In theory Orthodoxy could choose to accept some or all Reform Jewish comversions, if the Reform and Orthodox community worked together and had common standards. In fact, in the 1950s Rabbi Joseph Soloveitchik (Modern Orthodox) and other members of the Rabbinical Council of America (RCA) engaged in negotiations with the leaders of Conservative Judaism’s Rabbinical Assembly, including Rabbi Saul Lieberman. Their goal was to create a joint Orthodox-Conservative national beth din for America. It would create communal standards of marriage and divorce. The hope was that it eventually could become a standard for all sorts of inter-denominational life cycle recognition.
It was to be modeled after the Israeli Chief Rabbinate, where all the judges would have been Orthodox, while it would have been accepted by the larger Conservative movement as legitimate. Conservative rabbis in the Rabbinical Assembly worked created a Joint Conference on Jewish Law, devoting a year to this effort.
According to Modern Orthodox Rabbi Bernstein, the major reason for its failure was the Orthodox rabbis insisted that the Conservative Rabbinical Assembly (RA) expel Conservative rabbis for actions they took before this new Beit Din was formed, and the RA refused to do so. (Bernstein, 1977) According to Orthodox Rabbi Emanuel Rackman, former president of the RCA, the major reason for its failure was pressure from right-wing Orthodox rabbis, who held that any cooperation between Orthodoxy and Conservatism was forbidden.
In 1956, Rabbi Harry Halpen, of the Joint Conference wrote a report on the demise of this beit din. He writes that negotiations between the Orthodox and Conservative were completed and agreed upon, but then a new requirement was demanded by the RCA: The RA must “impose severe sanctions” upon Conservative rabbis for actions they took before this new Beit Din was formed. Halpern writes that the RA “could not assent to rigorously disciplining our members at the behest of an outside group.” He writes that although subsequent efforts were made to cooperate with the Orthodox, a letter from eleven Rosh Yeshivas was circulated declaring that Orthodox rabbis are forbidden to cooperate with Conservative rabbis. (Proceedings of the CJLS of the Conservative Movement 1927-1970 Vol. II, p.850-852.)
The plan may have been doomed from the beginning, as some Orthodox leaders held that not a single Conservative rabbi was qualified to sit on such a joint beit din. Few Conservative rabbis were willing to accept this view. See
http://www.joshyuter.com/wp-content/uploads/2011/08/Saul-Lieberman-and-the-Orthodox-41.pdf
