Not really. The Russian Greek Catholics are subject to a Roman Catholic bishop in the USA, but there are two congregations in the entire country. Many of the Byzantine Ruthenian Catholics are staffed by Latin Rite priests, not a bad thing but some don't get the pyrohy and ethnic traditions.. the ones I know are great Greek Catholic priests even if their background was Latin-Rite.
As we may know the common story is that St. Alexis Toth was a Greek Catholic priest in the USA. He was subject to the local Roman Catholic bishop that didn't accept certain provisions... then you had a large number of adherents go to the Orthodox Church then.. then later due to more provisions the Greek CAtholics left and founded www.acrod.org
The American Carpatho Russian Orthodox Diocese.
So it's been a battle here with the Greek Catholics being able to carry out what was written in their original "unions" with Rome forever, it still goes on about whether to have married priests or not etc...