You won't be able to integrate them unless you're bigger than them. Also you'll never be able to integrate them if they have a Heathen religion. Byzantium starts as Christian, right? So make sure you never convert to Muslim or anything else
In case you're not aware, the PU will break if, when your monarch dies, either is true:
- Austria's opinion of you is negative
- You have lower than 1 Prestige
So you will want to Improve Relations with Austria immediately unless they're opinion of you is already good, and keep an eye on that over time. You want to keep your Prestige high in the game anyway, so that is unlikely to be an issue, but if you ever do lose a war and it goes low or negative, take immediate steps to get it high again, like fighting an easy war, or revealing some new TI if you have Exploration and Quest for the New World.
There shouldn't be any coring issues. When you integrate a PU/Vassal, all of their cored provinces become your cored provinces.
The only coring consideration is if you feed new territory to your subject (which is a good idea) - once you do, make sure you don't integrate until the subject has cored it all.