I asked my Byzantine Catholic bishop, and he was against that. He said that you can ATTEND liturgy in Orthodox church, but you cannot RECEIVE the Communion, and Communion is the most important part of liturgy. He said that Catholics should go to Catholic churches, because they share the same FAITH. Orthodox church negates many Catholic teachings and dogmas, and I know that in my local Orthodox parish, priests are not in good relations with Catholics of both rites.
Bishop said to me: āWhy should you go to the people that call you heretic, when you have over 100 Catholic churches here and you must go to Catholic church on Sundays.ā
My bishop and whole Byzantine Catholic church in my country is very traditional, and all Byzantine Catholics attend ONLY Catholic liturgies or masses, especially on Sundays, both Roman and Byzantine. A very few of them visited Orthodox church, I visited it only once, when I was buying chotki in a monasteryā¦ I even know a person that was KICKED OUT of the church only because he was Catholic.
So, the final answer to your question would be NO, Eastern Catholics attend only CATHOLIC liturgy or mass on Sundays, but they can attend liturgies if they want, that is not a sin, but on Sundays they must go to Catholic church.