Supply line sweating above one piece tub/shower combo
I just pulled a one piece fiberglass tub/shower unit from one of my bathrooms to fix a suspected drain leak and convert to a shower only unit.
I had been noticing moisture buildup for a long time towards the drain end of the tub. I suspected a drain leak, but after I removed the unit, I found that the supply line crossing over the top of the unit was sweating. It looks like the line was sweating and then running down the cold water supply to the fixture and dripping onto the concrete floor.
The unit does have a light in the ceiling of it, and the edges have never been trimmed out. That's the only place I can see that would allow air to get up into the cavity.
I see no evidence of the line sweating elsewhere above the drywall ceiling, only over the tub/shower unit where the pipe is open to the air around the unit. This bathroom is rarely used as it is in the basement and has never been fully finished (hence the concrete floor).
I have evidence of water on the bottom plate of the wall and the nailer that the edge of the unit was attached to.
So, my big question is if I drywall the ceiling and walls behind the new shower unit, should that seal out the possibility of warm/moist air reaching the supply line as is with the rest of the plumbing? I was even going to go as far as putting some pipe insulation on the cold water line to help.