Yes it's true
But even with out Islam there is still nomadic desert people ( who I won't say jiat in case you do read my timeline)
That can be big problem they realisticly would not take as much land as the Muslims but the war and the lost territory would diatact the Byzantines enough to allow the lombard to take nother italy
I don't think disunited Arab tribes of different religious sects, not under a central authority would really be enough to make the Empire lose complete control of Italy personally.
Afterall, the Empire held onto the Exarchate for over 100 years IOTL, despite all the shit they were going through. They held onto Southern Italy all the way until the late 11th Century.
No Iconoclasm also means that the Papacy will be considerably less hostile to Constantinople, tensions will still exist, but they will boil over much later.