No, the insulation shouldn't touch the drywall. Insulation is created to regulate temperature; if it touches the drywall, it's going to soak up moisture through the air, which may result in mildew and mildew growth. Use adhesive into the back on the hatch and press a bit of rigid foam https://raymondel3n3.laowaiblog.com/31380639/5-tips-about-insulation-installation-you-can-use-today