How could we make this work with shopify apps?

Hi, Short answer; you probably can't.

You will need to be able to send us the email of the person when they start using your add-on. Which as far as I know not possible with the possibilities Shopify gives you.

If you are able to add a tracking script to your page + the conversion snippet in the signup form we can make it work. Again, as far as I know, this is not possible but I'm hoping here I'm wrong.