Can my customers edit a design even after it has been added to the cart?

Yes, they have an edit link in the cart that send them back to the customizer.

See this video below showing the process: 

IMPORTANT

• It works by default on all platforms but Shopify. Shopify users can contact us to [e-mail] to get this activated.

• The feature is not available for PrestaShop 1.6 but it works with PrestaShop 1.7