No, you should not install greenboard over a poly vapor barrier on the exterior wall behind the tub. Here's why:
Code & Safety Issues:
- IRC P2715.4 requires bathroom exhaust fans to be ducted to the exterior, but doesn't address wall construction.
- IRC E3405.1 requires a vapor retarder on the warm-in-winter side of insulation in climate zones 5+.
- Installing poly on the exterior wall creates a double vapor barrier when combined with interior paint/drywall, trapping moisture.
The Real Problem: Your damp walls indicate the exhaust fan isn't removing enough moisture. Adding vapor barriers will make this worse by trapping moisture inside the wall cavity.
Correct Approach:
- Fix the fan first - Check if it's properly sized (minimum 50 CFM for bathrooms, per IRC M1507.3) and ducted to the exterior
- Use greenboard or cement board directly on the wall (no poly)
- Ensure proper insulation in the exterior wall with the vapor retarder on the interior side only
If you must add moisture protection:
- Use a smart vapor retarder (like MemBrain) instead of poly
- Ensure the wall can dry in at least one direction
The dampness is a ventilation issue, not a wall construction issue. Fix the fan before modifying the walls.