That build process can be done using TravisCI for free, provided the GitHub repository containing your Hugo base is public (and why wouldn't it be?) This removes the need for that Droplet and its associated cost.
Nice, good to know. I'll use Travis in the future for some side projects. But for my site/blog I think I'll stick to using my current droplet because I currently have no build time delay, and hugo is very fast. As soon as the push to github is complete, I just refresh my browser and the changes are in. With Travis it appears all open source projects share the same build queue so it can take minutes for the changes to take effect.