The Normans succeeded when they were able to put down roots somewhere, become integrated into the local political culture and become intermarried with the existing power brokers, and hit at a moment when the incumbent power was weak or in turmoil
The late 11th century does describe Fatimid Egypt like that on the last point. But projecting power across the Mediterranean like that - it's no easy lift. There'd have to be Byzantine or Venetian support, both of which are coming with massive strings. I suppose if they don't go to Epirus but instead to Egypt, they might be able to get the Byzantines on board, who frankly needed all the Allies they could get post Manzikert.
The issue is that unlike the various mercenaries and slave soldier groupings that formed the Praetorian basis of rule, really for most of the middle ages in one way or another, in the various Egyptian states and dynasties, the Normans are unlikely to fit into that role. They're Catholics who in Sicily have a Kingdom of their own. They're not likely to get on well with the large landholders and court officials who formed the basis of Egyptian state capacity, because the Normans wanted all the land they could get their own hands on.
Could they topple Fatimid Egypt? I think so. They won against far worse odds before, after all, and tactically speaking the Normans tended to do quite well against Arab armies. But could they hold it?
That, I am not sure of. The Seljuks could swoop in and then that would be that. They'd be far away logistically from Sicily and would have difficulties with rebellions. Their allies in the region would be likely to double cross them. They don't fit in well with the local aristocracy.