I think this is probably one of those "Oh sweet christmas yes" PoDs for the Romans in terms of long-term survival, assuming Bela inherits Hungary. Hungary is basically another Balkans or Anatolia, not in terms perhaps of population density (yet), but another base from which to operate from. Its security within a Roman sphere is "Is the Danube Friendly?, Secure the Carpathians, Secure the West, Secure the Prutha." Which works very well with a Roman Balkans as the Danube is friendly, and also is interested in securing its west, which is common with Hungary, and the Pruth serves as protection for them as well.
Basically, Roman Hungary can reduce its overall defensive concerns to working with the existing Roman strategies west and east, whilst strengthening the Carpathians. The entire idea of securing the Danube disappears for both parties, and suddenly they have freer hands to resolve long-term defensive problems. (i.e. fortifying the Carpathians, send forces to secure Anatolia, support Italy against the HRE, etc).
You take that ability to secure common concerns, and then secure Anatolia? Suddenly you have not just the Balkans, but in the long run the Balkans, Anatolia, and Hungary as major regions for the Empire to recruit forces from. Ignoring that we've more or less undone Manzikert, with the exception of those new Turkish settlers who could be converted, this is an Empire that can really flourish in the long term.