[brndn]

If you are showing a demo or something, you can still navigate to your DO IP address. Of course, I don't know if other things (images, etc.) on your website also rely on their DNS.

[Maakuth]

For that kind of emergency, you can point the domain name to the IP address via /etc/hosts (there's a similar file in Windows as well).

[tracker1]

c:\windows\system32\drivers\etc\hosts