Yes, they just need to click on the "Save Design" button.
If the user accesses the store using an account, the design will be saved in his account and in the merchant's Zakeke back office (and you can access those designs from the "Customer Saved Designs" section).
If you do not require users to create an account to access your store, the design will be saved in the cache and users won't find it there if they access the customizer from a different device or they clean the cache.