Like @gp+digitalocean said, if you mean that the server has a static IP, then the answer would be yes.

You can safely point your domain to the IP without any interruptions from the IP changing (because the IP is static, meaning that it won’t change).

Also, DO doesn’t change your IP address when the droplet is shut-down or restarted. I believe that you lose the IP address assigned to you on droplet creation if the droplet is deleted.

Your two questions are less related than you think, but yes the IP you will get is “static” (hence why you’re not running a DHCP client)