Can I add a supplementary product to the checkout page on my app?

[Esquire1]

Hello,

I’m creating a Shopify app whereby I’ll be offering a supplementary product to the user when they’re checking out. This product is not linked to the store nor is in user’s product catalog. 

My question is if it’s possible to show that product on the checkout page? If the user selects it, it’ll be added to the cart which the user can checkout as normal. Preferably a single line item on the checkout page like:

- Add X to this order for $59.00

[Esquire1]

Thanks for these details, however, I’m researching if this can be done programmatically. Specifically, if I’m making a Shopify app, can that app add items to the checkout page?