WI/AHC: Robert Guiscard/Bohemond d'Hauteville becomes Byzantine Emperor

What if Robert Guiscard had not went to the aid of the Pope against the HR Emperor and had instead focused his efforts on Byzantium. With a bit of luck, Alexios is slain allowing Robert Guiscard to roll through the Balkans laying siege to Constantinople before the city surrenders and he is crowned emperor. And what if after his death (which would be delayed), Bohemond is able to secure his own position as emperor maybe by taking a Greek as his wife and fighting against Roger.
 
Maybe Byzantium could be brought into the Catholic fold. Would the pope and other Western leaders push for this? On the other hand maybe Robert would turn towards the eastern rite inorder to consolidate his holdings?
 
Maybe Byzantium could be brought into the Catholic fold. Would the pope and other Western leaders push for this? On the other hand maybe Robert would turn towards the eastern rite inorder to consolidate his holdings?
Robert seems to be the type to convert in order to consolidate his holdings, however, he did in OTL build many Catholic churches and played an instrumental part in making southern Italy follow the western rite. I think it would be more likely that Bohemond would convert to the eastern rite in order to gain the support of the populace against his brother, Roger.
 
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