I might be over thinking this but I think there would need a Stored Procedure linked here somewhere.
So what I was thinking was to send a Schedule Report to a group, for example having a group that's members have items in the cart.
Then the issue is, how can I get the users in that group as we would need to add them to the linking table (User group) as you know we this is sometimes done with a SP for after a data import has ran.
So we could use the same type of SP, but obviously only looking for users that are in the tps_shopping_cart table (in the table there is a tps_user_guid).
Also you would have to make sure you remove the users after the report was sent maybe with another SP to run later, again I guess you could do some of the SP within the product but I feel you would need SQL at some point.
There will be other ways to do the same task, but this is my first thought.