There was no Armenian Catholic Church until around 700 years after Gregory died. He was a member of the Armenian Apostolic Church which is part of the Oriental Orthodox communion. They have not been in communion with Rome since AD 554.
PiusV is correct, Bayard, as is NRx. Interestingly, however, if +Gregory were to arrive at my Greek Orthodox parish Sunday and approach for communion, the priest would give him, as he would, say, a Copt, the holy gifts. He cannot give them to a Latin, though I understand that a Latin priest would give them to me.
It has to do with the nature of what seemed to be Non Chalcedonian theology vis a vis that held by the rest of the Church at the time of the Council of Chalcedon. Orthodox and Oriental Orthodox theologians have now come to understand that the differences are in the way we talk about the natures of Christ rather than in what he hold to be dogmatically true. Thus, a Copt, for example, or an Armenian, can receive in an Orthodox Church if there are no Oriental Orthodox churches reasonably close. The ecclesiology of the Latin Church, probably more than any theological issues, is what keeps our bishops out of communion with the Latin bishops and thus prevents us Orthodox from communing Latins or receiving communion at a Latin Mass. On the other hand, I am quite confident that lightning would not strike if piusv received at an Orthodox Liturgy or I at a Latin Mass. I do think it would be inappropriate, however.