No, DigitalOcean cannot and does not provide a backup plan for droplets as due to the nature of how the their infrastructure works. It would be a sys-admins nightmare!
Backup plans are available to the end-user, yourself to setup and configure. You can create your own using space, volume storage, or the built in droplet snapshots/backup feature.
However this is up to yourself to do.
For example, one project I have running in one droplet is a website that has a cron triggered bash script that drops the database and copies the files of a site to a mounted volume daily. Additionally I am using the DigitalOcean snapshot/backup feature for the server to take a weekly snapshot.
Here is a great start to help with a backup strategy.
When dealing with any kind of important data, it is essential that you implement a backup scheme. There are many different ways to back up data on a VPS. In this guide, we will discuss some ways that you can backup your data and discuss the merits of the different options.