It would probably resemble Andalusian Romance or Maltese to a degree when intermixing with Latin. Given that the eastern empire was heavily Aramaic and Greek, I'd imagine that many Arabs might actually adopt Aramaic outright given the shared origins or mix Arabic with Greek in akin to Cypriot Arabic / Sanna or Cappadocian Greek.
Edit: Of course, that's just linguistics. The Arabs being Romanized culturally would depend on significant infiltration of Roman society akin to the Germans, rather than the initial cultural separation they practiced during the Islamic Conquests that slowly led to the cultural assimilation and homogenization of client cultures and communities.