The Persian Empire was the only one officially recognized by the Roman Empire. The Persians would no more be "swallowed up" by the Arabs than the Romans would.
The Ostrogoths and Turks were brought into the Roman Empire as foederati, as allied tribes owing military service to the Empire. The Ostrogoths took over Italy. The Turks took over Asia Minor.
Rather more than just the Persians, no?