Well, main story wise, no. However additional side content is possible to miss. But that's usually just small things. One thing I know for sure (because I played through 3 times now) is when Ashles took you to the clocktower, when her affection (I think it was affection, maybe another trait) wasn't high enough, you don't have a special option in your answers and miss a small extra scene. Those options usually have a different color. Since this scene is a one-time event, once you're through it, you can't do it again. So if the traits aren't high enough, you may miss some minor additional scenes. But storywise you don't need to worry.
Are you sure you are not thinking of the restaurant scene? Because that one has a yellow option locked behind exhibitionism, and it doesn't appear in the gallery, so it's actually a one-off... But there are no yellow options in the clocktower scene.
Unless it's removed entirely if you don't meet the prereqs, but usually that isn't how it works.
Edit: tested on a fresh game, and nope, that was correct, and indeed you don't get it in the Gallery on replay.
There is a yellow option that is unlocked at, I think, Exhibitionism 11.
So, yes, it is technically possible to miss content.