Yes but a large empire doesn't always expand into a fragmented area and incorporate it successfully. Remember Justinian's invasion of Italy?
I think this depends on what happens to Frankia.
Merovingians were incredibly divided and unstable. More like 4 seperate states, than a unified empire. With Neustria and Austrasia endlessly infighting.
The Caliphate itself doesn't need to annex Frankia. Just split it between Saxons, Avars and potentially western Slavs. Ending Europes only remaining major power.
Their ardent paganism would give them no religious incentive for a reconquista. Actually relations with the Caliphate would probably be cordial, since they helped them in expanding their territory.
Without Frankia, there would be no major force to push back against the later divided Muslims. Since Europe would be just as divided as the Muslims.
I'm inclined to think that the Caliphate, with the Byzantines out of the way, could establish rule over the Mediterranean for a generation, but I see it collapsing and not returning after that. In our world the Abbassids never got Spain back; so the probability of the successor-regime of this Caliphate getting back Italy seems pretty low.
Firstly, the Caliphate wouldn't lose 100k men in 717. And wouldn't lose 740 Akroinon. (Battle of Ardabil could also be butterflied away?)
This means the Syrian army, the powerbase of the Umayyads, would have a much larger manpower advantage over the rest of the provincial armies.
This would mean the Yaman tribes would retain a massive advantage over the Qays. Making the 3rd fitnah unlikely to happen. With Yazid iii becoming Caliph largely uncontested after Walid ii's assassination, preventing the civil war.
Without the 3rd fitnah, Khurasan would be far more stable with alHarith ibn Surayj being defeated soon after beginning in the 730s. Allowing Nasr ibn Sayyar to retain complete control of Khurasan.
Easily preventing Abbasid propaganda from swallowing the region.
Beyond that, one of the main reasons why the Khurasanis revolted, is since they were forced to endlessly fight incredibly difficult battles with the Turgesh Turks, with major losses in the 730s, getting little booty even in victory.
Syrians had a much easier lifestyle, with a relatively easier foe (Byzantines) and dramatically more loot.
The Khurasani felt sidelined by the regime.
But 50 years after the conquest of Constaninople, the Caliphate would have much more manpower which it can send to bolster the Khurasanis, preventing Turgesh victories. Thereby reducing Khurasani grievances.
But even if the climate is suitable for revolt, why would the Abbasids focus their propaganda on Khurasan
only, and not also the Mediterranean?
OTL, the Berbers had already become independent from the Caliphate, 4 years before Abbasid propaganda began. But compared to Khurasan the Maghreb and even Iberia were blackwater.
ITTL, the Mediterranean would be the heartland of the Caliphate, not greater Persia.
So it would be stupid not to propagandise this region also. The Berbers would likely be very receptive to this, since the Umayyads were enslaving their womenfolk as sex slaves, despite being Muslims....
Given that the Berbers dominated iberia and the maghreb. ITTL they would probably also dominate all Italy and southern Frankia. Basically the entire western med.
Thus Berbers from the east and Khurasani from the west, should be able to Reunify the entirety of the Caliphate...
But this TL's Berber revolt could be more successful. Establishing an independent western med by 740 (though they'd need to include the Arab garrison's far more than OTL, or else they'd put up a life or death defence at all costs)
But the greater manpower without the 717 loss, might allow the Berber revolt to be crushed in its entirety. And the region overall would receive more focus with a capital at Constaninople and a larger Mediterranean navy.
A lot also depends on how long the Caliphate's central authority holds together for. When the Caliphate goes to pieces (this might take a few centuries, but it will happen) how Islamicized is what used to be the Byzantine Empire?
The collapse of the Caliphate was mainly due to Mamun's idiocy.
The Amin-Mamun civil war, ended the brightest era of the Abbasid golden age.
With Baghdad being devastated by a year long siege, as well as Iraq and much of the Caliphate in general m as well as various revolts all over the empire.
But after winning, Mamun tried to rule the Caliphate from Merv. In modern day Turkmenistan. This is one of the stupidest descions in the history of the Abbasids. With Iraq and everything west of that being in anarchy.
After 6 years at Merv he finally moved back to Baghdad. But first, he appointed Ali Ridha, the Shia imam as his successor alienating most of his powerbase. Then he killed him, alienating most of the Shia.
He proactively decided to give his governors
Hereditary Governorships with more independence like the Samanids and especially the Tahirids - who now controlled his own powerbase of Khurasan.
Why you would want to set up
semi autonomous monarchies within your own state baffles me.....
Tahir didn't actually even listen to Mamun, not wanting to march against Babak Khorramdin a
Zoroastrian revivalist who had taken Azerbaijan....
Mamun was
powerless to force his governor and army chief to actually do anything, so he needed to rely on his brother Mutasim.
Mutasim had built up a professional slave army of Turks. And was a military man. Mamun was heavily reliant upon him for the rest of his reign. With Mutasim succeeding him.
The Turkish troops were highly effective, but unloyal. If a Caliph went against their wishes, then unlike other local armies, this would be an existential threat. Since other than the army, they have no relatives to help them or a trade to support themselves. Most of them didn't even know Arabic, and were hated by the general populace - which was why Samarra was built.
Hugh Kennedy describes them as acting in
desperation for their livelihoods, which is why they took such drastic measures as murdering a Caliph.
Beginning the Anarchy at Samarra which lead to complete disintegration of the Caliphate.
This occuring is contingent on so many different things, that could be easily butterflied away.
In the lead up to disintegration, the Caliphal administration was gradually improving and becoming far more professional and developed. With bureaucrats beginning to gain more influence than the military aristocracy.
Without the anarchy, the Abbasids would become far more of a bureaucratic. Being dominated by scholar officials like Song Dynasty China. Which would improve taxation efficiency and central control
Unlike the song, the only major external threat the Abbasids have are fairly distant central Asian Turks. Who would have to cross perilous deserts and the mountains of the Zagros to reach the Abbasid heartland. (Byzantines were only able to go on offensive after complete disintegration in 960s)
Beyond that, non Arabs were beginning to convert to Islam en masse - giving a potential massive manpower surge, if slave armies never emerge.
But assuming it still collapses, the islamification of the Byzantine domain depends on when it occurs. But generally, the great urban metropolises would be dominate Muslims. Smaller cities would have Muslim minorities, while rural regions would be entirely Christian.
Though this depends on the Greek social cohesion. Copts were an incredibly tight knit community after facing discrimination from the many foreign empires which had ruled them for thousands of years. Such as when they chose Monophysite Christianity and were persecuted by Romans, but held fast.
I don't know if the Greeks of Anatolia would have the same cohesion allowing them to withhold assimilation.
Inlstead they could be more similar to the Andalusi Christians, who culturally assimilated into Arab high culture, speaking a form of Mozarabic.