In a scenario where the Byzantines win Yarmouk or otherwise repel the Caliphate's invasion, it seems likely that they could hire Arab and Persian foideratoi; Christian and Jewish Arabs emigrating from the Caliphate, some originating from the Ghassanid realm. As well as Christian, Mazdaki, Khurammite, and Zoroastrian Persians originating from Iran, some of whom may resettle in the Byzantine empire after the fall of the Sassanid Empire. For example, mercenaries/nobles like
Theophobos. Thousands of aristocrats and religious emigrants from the east could be employed as cavalry
tourma and settled as an additional source of manpower.
While the Byzantine Empire is at the time occupied with re-establishing its defensive lines in Syria and Palestine, could the use of Arab and Persian foideratoi establish a decisive advantage against peoples like the Bulgars, Lombards, and Visigoths? How long would it take for Heraclius to re-establish the frontier, and how soon can Byzantine Emperors start looking west? Or will they ever look west again?
As an addition to the typical Yarmouk discussion, here's an interesting passage from
Byzantium and the Early Islamic Conquests (1995) by Walter Kaegi:
"Islamic tribesmen did not simply overrun a static and gravely weakened Byzantine Empire. Instead, their invasions occurred while Byzantium was still in the process of restoring her authority over the full extent of the former eastern borders of her empire. Heraclius was in that region because he was personally involved in overseeing that restoration and reunification. If he had had more time, he might have succeeded. The Muslim invasions caught him and the empire off balance at a very awkward time, and kept them off balance. The exertion of minimal pressure at the critical moment and place was able to bring the Muslims maximal rewards in terms of military victories and territorial conquests, with a minimum of casualties. The Byzantines were just restoring their authority in the Syrian cities and countryside, but that process of restoration and creation of lines of authority and a viable power structure with conscious identification with Byzantium was even more tenuous in the areas east of Jordan and the Dead Sea when the Muslims began their own probes and raiding, which they very soon greatly intensified." (pg. 87)
So in this scenario we can perhaps assume that either Yarmouk was a smashing Byzantine victory, which is slightly unlikely but not impossible, or we can assume that it never happens at all, and the early Arab-Byzantine conflicts are delayed by a few years, allowing Heraclius to re-establish his control over the borders. At which point the Byzantines can win defensive battles. Either way, the situation appears similar though, as Byzantine aggressive moves will occur only after the Sassanids fall.