Short Answer: Technically, if you had the funds to do so, but there would be no point.

Long Answer: For the majority of its history, the Byzantine Empire was Catholic; the Schism that divided the Church into Catholic and Orthodox halves is typically given the date of 1054, though the conflict that caused it predates the schism by a good while, and it appears that inter-faith relations were less immediately affected than it might seem. Eventually, by the late 12th-early 13th century, relations had degraded significantly.

More to the point, however, excommunication was (and is) an ecclesiastical punishment, not a secular one. It theoretically doesn't matter what nation you were in. The punishment (for Catholics) included exclusion from certain sacramental activities (such as partaking in the Eucharist), being shunned by other Catholics, and the like. It should be noted that the Orthodox church can also excommunicate, although it is a lesser punishment than in the Catholic Church, since major heresies are punished by anathema in the Orthodox churches.

Excommunication is supposed to be 'medicinal'- it is expected that the social and religious pressure of the decree will force the subject of the excommunication back into the fold. In excommunicating someone, the Church was stripping away all of the rights they were afforded as a Christian, effectively.

Fleeing to a non-Catholic country would really just be doing the same to themselves! A Catholic in the Byzantine Empire after the Schism would be seen as a schismatic by the Orthodox Church and (after 1438) would still be seen as excommunicated by the Eastern Catholic churches.

Furthermore, excommunication was usually used either for political reasons or against heretics; in the latter case, you'd hardly be better off in the Orthodox Church (the Orthodox and Catholics view each other as schismatics, not heretics, and anyway Orthodox Christians can't be excommunicated by the Catholic Church because they're not in communion with the Catholic Church to begin with), and in the former case you have a deep vested interest in your current position, and thus probably don't want to abandon it to flee to another country.

This is doubly the case because, in your question, you specified excommunication by the Pope. For the Pope to personally issue an excommunication, the subject in question would have had to have been very powerful, or (in the case of mass excommunications) very widespread. Smaller potentates would be excommunicated by local bishops or ecclesiastical councils; the Pope would typically get involved when it came to condemning the likes of kings and emperors, and exceptionally widespread heresies, like the Cathars.

Especially in medieval Europe, where wealth was heavily tied to land, fleeing excommunication really didn't make sense most of the time. If you had the wealth to actually flee to the Byzantine Empire (post-Schism) you were giving most of it up to do so, and when you got there you were still excommunicated and unable to take part in the sacraments of the Catholic Church and now surrounded by members of the Orthodox Church, which considered you a schismatic.