No, the insulation shouldn't contact the drywall. Insulation is designed to manage temperature; if it touches the drywall, it is going to take in dampness from your air, which can cause mould and mildew advancement. Apply adhesive towards the back with the hatch and push a piece of rigid foam https://webtagdirectory.com/listings13044558/the-2-minute-rule-for-insulation-installation