No, but it's quite difficult to have email reliably and consistently delivered to Gmail and other major email providers without sending it via a relay. The relay provider is in the business of maintaining IP addresses with good reputations that aren't blocked by spam lists etc. If you can find and keep a reputable IP address, then you're fine, but it's usually easier to pay someone who does that for a living—you have no guarantee that the IP address assigned to you by Digital Ocean or whoever wasn't used for spamming at some point.
This is also why I went with Vultr as my server host. They block port 25 by default and make customers file a support ticket with them to unblock that port. They also require your account be active for at least a month and be using their service in good standing during that time. Wasn't an instant process, but was simple enough to accomplish in the end.