I wouldn't get hung up on the "canon rule" that "If it is on-screen, it's real!" in all cases.
There are shots with equipment shadows, jiggly walls, the mat used to break a fall, etc.
In the case of the Enterprise bridge, there are a precious few instances where the camera tilts up, but this was not a highly finished part of the set which was intended to pass visual scrutiny. If your eyes are where they are supposed to be (i.e., watching the characters), you should only be catching the ceiling in your peripheral vision.
Consequently, the nature of the dome is open to question.
We've seen at least one transparent dome (Generations). It might be a sensor dome. It might be translucent. It might be transparent. It might be some combination (i.e., flip a switch and it polarizes to keep out light).
There is room for interpretation here.