OK, let me create a secenario here.
In 900, the Byazantines invite th Magyars to N.Italy in order to smash the Lombards. they conqure Italy from The Papal stats to the alps, from Milan to the sea. Verona is their capital. Lets say that hungarian remain their language (but with romance influance). Bulgaria controls Panonia.
What then happens? would they follow the pop or the empror in the great schim?
As for the language, they would most likely shift not beyond a couple centuries to a Romance language, probably a Northern dialect of the Lombard or Venetic type rather than Tuscan. They would find themeselves among a Romance-speaking majority, and would also Christianize pretty quickly - unless they go straight for Rome to crush the Papacy, which the Byzantines definitely would not find funny, despite all their animosity.