Yes, but not immediately. Once you cancel your paid plan with custom domains, your links and neon pages will continue to work until the last day of your billing cycle. After that, your links and pages will still be displayed as “untitled/xyxyxy” in your account.
They will not work anymore but are stored in case you want to re-use them with another domain. To re-assign your links and pages to a custom domain you can either reactivate the same custom domain you’ve used before, or you can open the edit tab of your link and click on the “Use custom domain” field, then choose another domain and you’re done.