When you upgrade a package from outside of the official repositories, there's always potential for breakage. The reason why stable releases of Ubuntu don't continue to add new upstream versions is to stay with a well known and tested set of packages that work together. That said, I don't see any reason that a new Nginx will break Ghost.
The great thing about DigitalOcean is that you can spin up a droplet quickly to test something and then destroy it. Since you're only changed per hour, it's very cheap to test things before you do it to your production server. I just spun up a Ghost droplet and added that PPA. It reinstalled the default, Nginx config which took precedent over the Ghost config. So I had to remove it:
sudo rm /etc/nginx/sites-enabled/default
sudo service nginx restart
And the Ghost blog was up and running.