I would imagine that specialty restaurants will be closed at some times for filming, maybe late some evenings. Same with some other venues. I can see the young cast set up at areas like wake-view, vista lounge, sanctuary, in the Suites, etc. I heard that they had set up in a section of the Sanctuary. I believe that a lot of scenes will actually be filmed separately and at very late or early hours. I can tell you that scenes of hoards of unsuspecting 'average' princess cruise guests are NOT what they will be wanting. They will have set up carefully crafted and scripted dates and events in the different venues. And would not do this during prime hours. I know that the Batcherlor/Batchelorette sometimes film overnight.
How much this would impact the overall cruise, I don't think anyone knows.