No, not necessarily. You can add the ‘Fan Pass Gated Product’ app block to your default product template and it will only appear for products that you have configured a gated discount within the Fan Pass app.
This is not to say you can’t set up a new product template for your gated discounts to further customise them and give them a unique look and feel.
Check out this Shopify article that explains how you can create and assign a new template to your gated products.