DNS-01 challenge for a provider not in the supported provider list

Probably yes. I used to work with this solution to serve custom error pages with Nginx. It works fine as long as you have a wildcard cert in place. If not, bad URLs such as not-existing-url.example.org will correctly trigger an http 404. However, since there is not a valid service under not-existing-url.example.org the page 404.html will be served with the Traefik default cert (self-signed).