No, the insulation should not contact the drywall. Insulation is intended to manage temperature; if it touches the drywall, it will eventually soak up humidity within the air, which may lead to mildew and mildew development. To treatment this and prevent moisture problems, wrap the plumbing with foam pipe sleeves. https://edwinmv6w6.theblogfairy.com/31558488/5-simple-statements-about-insulation-installation-explained