As I said above, the Qur'an seems to be a partisan of the Roman Empire and it seems likely that Muhammad envisaged his Hejazi community as becoming, like Ethiopia and Armenia, part of the Byzantine commonwealth in opposition to Sasanid imperialism.

I believe you're reading too much into that event. It was because it was a fight between Christians, who Muslims see as Kins of sorts called People of the Book and the Zoroastrians. He never envisioned joining the Eastern Roman Empire in any sense of union. When he sent letters abroad, preaching his message, he sent the letters to the Sassanid Emperor as well, offering him a similar message as the Emperor in Constantinople. When the vassal state of the Romans killed the Prophet's envoy, he sent an armed expedition to avenge that. That set the tone for the future conduct with the ERE. Don't forget, the Prophet promised the Muslims that they will come to conquer Constantinople and Persepolis. That's not the words someone seeking a union uses.