Yes, the dome had what is referred to as a weather casing. This protected the dome from the elements and as mentioned earlier allowed it to be lit electically from behind during night time hours when sunlight was not available to be harnessed. The lead glass windows on D Deck were also lit from behind at night. I imagine the dome would be a pain to keep clean had it not had this casing protecting it. Imagine being a first class passenger, looking up from the staircase and seeing bird poop on the glass ha ha ha ha
Not many people realize that the ship also had a second staircase at the aft end between the 3rd and 4th funnels. The weather casing was directly connected to the promenade deck and rose up to about shoulder height I think. You can see it in the background just to the right in the James Cameron film when Lovejoy is talking with Cal.