You would not be able to automate the process of determining whether individuals from your SunShop have also signed up for your AWeber account. When you export the file from SunShop and subsequently import those contacts into your AWeber list, you can utilize the “Update on Import” option mentioned in this related community post as well as the use the Tag on Import feature. This allows you to tag those contacts, which you can then search for on the Subscribers page.
It’s important to note that even if customers have made purchases directly, they must be aware and provide explicit permission to be added to your mailing list before you can import them. As you mentioned, if they checked the box to receive a newsletter to subscribe to your mailing list, then you are clear to import those customers into your AWeber account.
When I referred to sending emails outside of AWeber to request permission from customers to be added to your mailing list, I was suggesting the use of your custom domain-based email. You could consider utilizing Gmail’s “Send Mail As” feature with your custom domain-based email. I hope this information is helpful!