Yes. They recognize the authority of the pope and recognize that they are subject to his authority. They have equal standing as Catholics to anyone of us in the Latin Rite.
They accept all of the 21 ecumenical councils, as well as the Marian dogmas. By definition, we are one Faith; east and west may emphasize different things sometimes, but we all adhere to the same doctrine.
Although I am a Latin Rite Catholic by birth, and am presently involved in a parish authorized to use the Tridentine Mass, for the entire decade of the 1980's, I was attending the Melkite (Byzantine Rite) Catholic cathedral almost exclusively. They do not genrally use the "western" catechisms (Baltimore, the current CCC, etc.) since they have developed their own over the years. But they acknowledge the legitimacy of the western catechisms, just as the Western Church acknowledges theirs. As it is, the Melkite priests and bishop I know often quote from the CCC, even if it is more of a "western" work.
By the way, as I implied above, any Catholic may fulfill his or her Sunday obligation at *any* other Catholic rite from their own. You are free to attend the Melkites, Maronites or any other of the 23 Catholic rites any time you wish.
Thanks so much! I would love to attend Mass at one of the eastern churches, but I live in a rural area and the closest one is about 200 miles away. However, I will try to find one next time I'm traveling in any urban area. Thank you.