Romania would have probably collapsed if Egypt went down 640s, that would have been a blow to the economy it could not have sustained at that time, especially after losing the Levant post Yarmouk. Egypt gave the Empire breathing room for a while, and allowed it to slowly gain the upper hand against the Caliphate in the early 8th Century, and regain Antioch with parts of North Syria before the North-South split happened.
Without that, the Arabs could have probably smashed the Romans in the seas, and might have even been able to take Constantinople. It was already a close run thing in this timeline, with the Chalcedonian Syrian Kallinikos arming the Caliphate with liquid fire just because the Empire gave in to some Miaphysite Egyptian demands. Because of that thing alone, Roman control over the Med got seriously disrupted despite their strength over supposed desert dwellers.
One can argue that an early fall of Egypt would prevent those concessions and Kallinikos would aid the Empire instead. However, I doubt it would be the case. I predict that Arab fire ships would have sailed up the Golden Horn within a decade of Egypt falling, and Christendom itself would have been finished in the Mediterranean. Some holdouts in Sicily and Carthage might fight on for a while, but they will collapse soon enough. The Caliphate would march into Rome by mid eighth century by the latest. Slavs would probably go Muslim post the the fall of Constantinople, and Christianity would be confined to the Northwest of Europe, maybe just Brittania and Hibernia (assuming it survives at all).
Overall though, I think that world would be a richer and more educated one. Islam would then unify Europe, and considering how early it was-would probably get extensively Hellenized to a point where it would virtually become an odd Christian sect for practical purposes. So basically it would be a "Roman restoration" in all but name, what Justinian failed to achieve. That large centralized wealthy state could have promoted learning, and led to a more stable environment. Central Asia might not be conquered then, or even the Persian Plateau. I'd be surprised if Hellenic Islam was any more radical than some current "Christian" sects.
It could not have been any worse than the clusterfuck of OTL, between the Byzantine and Alexandrine Empires continuously fighting each other after Romania divorced itself, while the Exarchates of Carthage and Ravenna jump sides and the Persians and Arabs play spoiler. Yeah, the Med would be spared the horrifyingly destabilizing wars of Christendom, and actually get it's act together. Maybe it could actually lead to a world where China was not the global hegemon for 500+ years.