Domains mean nothing to devices, they use IPs. Domains are introduced to help humans remember addresses more easily. For an example, if you request domain.com, your browser will first look into it's cache, than it will pass to your OS resolver, if he has nothing, he'll then ask your ISP, if he's got nothing, eventually someone will knock on the doors of an authoritative .com server and he'll say something in the lines of: I'm not sure man, but ns1.digitalocean.com knows example.com, ask him. And since DO's NS has IP of your droplet matching example.com, he'll give your IP away and you're ready to connect to your droplet. Therefore, you cannot use domain if there is no Nameserver to resolve that domain to an IP.
Q: Can I use droplet's IP instead of the NS?