If the Huns hadn't fragmented on Attila's death, they would have once a) one of the Romes inflicted defeat on them, b) once the Germanic/Sarmatian/Proto-Slavic vassals tired of obeisance to the Khan, c) once a gavelkind civil war broke out or d) once a bigger, better steppe empire came along.
It was only after the Huns, Avars, Bulgars and Great Moravia that Pannonia, the base for whatever Hunnic kingdom would remain, was fully pacified by the Magyars. Even if they become Christian, I don't see a Hunnic Pannonia withstanding the next round of Turkic invasions well.
Now, if the Huns conquer somewhere else and settle there, they will quickly Romanize like the Goths and Franks and eventually become a Romance people (because they aren't subjugating all of Germany or Britain). If the Huns conquer Greece, expect a swift Hellenization and a probable Bulgar-Byzantine relationship until they are fully subjugated.