I see nothing mentioned in Article 330 regarding what you've proposed in a damp location. If you use PVC jacketed MC then it's suitable for dry, damp, or wet locations.
Per 310.10(C)&(D) have used weatherproof rubber-hole strain relief connectors, when owners planned to paint aluminum cladding w/ a weather-sealant paint.
Depending what owners tolerate, have also used UF cable w/ similar rubber-slot strain relief, when under eves or not subject to damage.
My jobs are too small & runs too short to order PVC coated MC cable, which is best outdoors. of course, it wouldn't hurt me to carry a larger roll on board for those rare jobs