Does the problem that Georgiou had due to the drift between the two universes not effect the ship?
Probably not - it sounds like it didn't actually travel through time the way Georgiou did - it just sat derelict in the wormhole for a few hundred years.
There was also the stuff in this episode about "two faces," one of which they say they have evolved past (or whatever their phrasing was). The Breen of this time could be a little more complicated than the Breen of the DS9 era. I assume we'll learn more about what that's all about later this season.