No, you can't download images from DigitalOcean.

However, you can take a look at User data scripts library. There you can find scripts that are used to install various apps on server.
Some of them are bash scripts, but some are CloudInit yml that can be used on with DO User data. You can customize bash scripts (maybe they even work without customization) an use it in VirtualBox and any other environment. This is not same as one-click apps, but will definitely help you set up.