Absolutely. For an application like Koken that relies on MySQL I would recommend going with at least a 1GB droplet ($10/month), should you see a higher load on your site you can upgrade via our control panel to a larger droplet.
DigitalOcean is un-managed and unlike shared hosting you are responsible for your server from the operating system up so having some knowledge of Linux systems administration is recommended.
When starting you can either use the PHPMyAdmin image which will provide you a graphical way to create the database that is required or you can use the LAMP one click image which provides all the software needed to run Koken but would require using the command line to create your database.
This guide will walk you through the installation process and you can reach out to us here if you run into any trouble.