Hi! I work for Code 42, makers of CrashPlan, and unfortunately I don't have any personal experience with Droplets directly. In looking through the support documentation and comparing to other similar situations, I would say that while it might be possible to install the CrashPlan client on a droplet, the additional cost of running it alongside your application would likely be significant.
CrashPlan uses a decent amount of RAM to monitor the files in your backup selection and back them up automatically. While this amount is small compared to today's Desktops and Laptops (or even a dedicated server), for a cloud service like Digital Ocean, it could easily push you into a higher pricing bracket and/or reduce the performance of your application.
If you wanted to back up using CrashPlan, it'd probably be better to set up a regular rsync process to send back to your computer, then use CrashPlan on that computer to send the backups offsite. DigitalOcean has provided instructions on configuring rsync here:
If you did want to experiment with CrashPlan on a Droplet, you'd want to use our unsupported instructions for headless installation and initial configuration. These are here:
This article provides a quick way to backup the most common things in a typical web hosting scenario: website files and database data. We will setup a full daily backup of a website folder and a copying of this data to a remote server (this can also work for another VPS). We will also set up a rsync example to just copy the incremental changes. Finally, we'll set up backup of a MySQL database.