Show block if user has never completed Ubercart checkout
I've got it figured out, at least for my own use-case:


I use a webform to collect info on the newly-signed-up user. That webform then redirects to the checkout page with the product in the cart. I used the Webform Rules module to auto-assign a "pre-customer" role to the user when they finalize the webform. Then, when they complete the cart checkout process, that user role is removed and the "customer" user role is assigned to their account.
I've got a block that is visible only to users with the role "pre-customer". That block is the one where they will be prompted to click a link to finalize their order/payment info.


Hope this can help someone else at some point! :)