yep, you can integrate a shopping cart with AWeber. For example my WP eStore plugin can be integrated with the AWeber.
But you kind of have to understand what sort of integration they are referring to here. What this integration means is that a person can be automatically signed up to your AWeber list. For example, when a customer makes a purchase using a payment button that was configured with WP eStore (e.g. membership payment) then you can make it so this customer automatically gets signed up to a particular list for future correspondence.
This does not mean that a visitor can put in his name and email address in the Aweber field and AWeber will pass those info to eMember so a member account can be created.
Let me know if my explanation helps understand the situation.