It would be unlikely, but not impossible. The Pope is the de facto patriarch of the Latin Church (he abandoned to formal title a while ago), which on practical matter requires an eastern-rite bishop who is an expert in Latin patrimony.
It is also complicated by the relationship of the western and eastern patriarchs, who are considered peers. The universal mission of the Pope is unique to the patriarch of Rome, which is liturgically Latin. It would take serious ecumenical discussion for an Eastern-rite bishop to be elected Pope without ecumenical harm.
From an ecumenical standpoint, Orthodox often consider Eastern Catholics to be at least equivalent to Latin Catholics, so having an eastern-Catholic Pope is irrelevant. The election of an eastern-Catholic bishop as pope would tend to reinforce the this view of Eastern Catholics as only superficially distinct from Latin Catholics. This would push the Orthodox further away from communion.
However, in a reunited church with the Orthodox in communion with the Pope, it would pose a difficulty to elect a qualified eastern-bishop as Pope, rather than as patriarch of his ascribed ritual church. Those who are currently Orthodox would see this as an intrusion on their autocephelousy, meaning that Eastern Rite churches would be reduced to administrative divisions rather than theologically and spiritually distinct churches.
