Can The Support Heroes apps work on checkout pages?

Unfortunately, Shopify apps cannot run on checkout pages and for that reason, the app can't be displayed on the checkout page.   

This is a Shopify intentional policy; therefore, no app can modify that without breaking the Shopify security 'requirements' stated at https://help.shopify.com/en/api/app-store/listing-in-the-app-store/app-requirements#a-security

Please note that  this applies to all Shopify apps, not only to The Support Heroes apps.