This is definitely possible even right now, we do this for the bitrise.io website & services too, as well as the CLI and other non mobile tools
Simply select Other as the project type during the setup, or if you already registered the project then you can change the Project Type on the Settings tab of the app.
Re basic linux container: use our Base image (https://hub.docker.com/r/bitriseio/docker-bitrise-base/). It includes everything required for the CLI and some useful preinstalled tools (like Ruby and NodeJS), and the image is pre-cached on the VMs so it takes no time to download.
You can also run
docker commands on the Linux/Android stacks, so you can just
docker run with any image you like (from a Script step for example).
If I missed something please let me know, but I think everything you described is already available, except the Penguin icon