Yeah, the decks are oriented along the axis of travel - this was something we had an interesting moment about on set, when we were discussing how the actors should be placed and react to something like a sudden acceleration. I pointed to the ceiling and said "you know you're traveling that direction?"
I can see the ship rotating or "banking" around 90 degrees, so that sometimes the saucer is nearly in line with the screen "horizon" and sometimes it's vertical. I don't see it customarily rotating anything like 360 degrees through a shot, although I suppose you never know - which is in and of itself one of the fun things about doing this: we don't know. We have no previous episodes or references to imitate, and it'll all depend on what looks and "feels" right.
Default orientation is vertical on the screen though - that was the little/big innovation Vektor
introduced that really sells this design as something different and special. Took me a week or two to wrap my head around it, silly as that may sound.