The scenario I'm suggesting is not Italy and Hispania, it's Italy instead of Hispania. It might have happened with different political circumstances in the dynastic politics.
This is even less likely.
After the fall of the Exarchate of Africa (698), most of the Byzantine navy and part of the armies located in the former Exarchate moved to Sicily. It would be logistically impossible for the Umayyads (they already tried) to attack Sicily from the sea with such amount of Byzantine military deployed there.
Since then, the Umayyads raided the area many times with little success. Sicily only started to become unprotected after the Isaurians relocated most of the Byzantine military force in the western Mediterranean to the East in the second half of the 8th century, when the Umayyads had just fallen.
The Franks seemed content with keeping the Umayyad contained in Iberia, with the Spanish Marches as a buffer. Besides, the Franks were not at their best at that point; the Mayors were still establishing themselves by weakening the royal institutions and bringing the country to civil war. There were still decades ahead until Charlemagne.
You are precisely mixing different eras here. The pre-Charlemagne Franks were not content at all, and they already held a long and exhausting campaign (725-760) against the Arab presence in southern Gaul.
The 'peace' with the Arabs did not come until the death of Charlemagne and the consolidation of the Spanish March during the early 9th century. Louis the Pious scrapped the Spanish issues from his agenda and was happy with keeping them at bay, while dealing with the long list of other issues he had to face in other parts of the Empire.
Honestly the posts that say every Christian soul in Europe would rise and march to free every inch of Italy don't explain how a large chunk of Christendom and Europe (namely Hispania but also, well, Jerusalem) was taken at that time without that much uproar. This is not the High Middle Ages. If one wanted to protect the faith, there'd be many opportunities among the pagan peoples in their neighbourhoods, or even their own neighbours. How entrenched was Papal supremacy by then, considering the Pope was basically under the control of the Byzantine Empire?
This consideration do not match with the most usual political and religious perception during that time. When the Arabs conquered the Levant (including Jerusalem) and Egypt, these regions had been dominated by non-Nicene Christian factions (= heretical) for decades and early Islam was perceived as a sort of (maybe extreme) Christian heresy. For many Nicene Christians the fact of Jerusalem being controlled by Miaphysites or Muslims did not make a big difference from a religious point of view. At least in the 640s.
Even if some European princes would have been outraged by the Muslim conquest of Jerusalem (it seems it was not the case) they could have been done nothing for stopping it, as it would be very difficult for Franks or Visigoths to send troops there. Apart that this was widely considered a matter to be dealt by the Byzantines alone, still the main Christian powerhouse.
And regarding the fact of the Papacy still being under the Byzantine umbrella it was considered something natural as the Byzantine Empire was indeed the Roman Empire, and it was logical that Rome and the Pope belonged to it. However, this did not prevent the fact that Franks considered the Pope as the maximum authority of the Catholic Church, politically tied or not to Constantinople.