No. CoreOS is a Linux distro focused on running applications packaged as containers (Docker or anything else) on top of it. It is so focused on running application in containers that it does not even have a package manager to install packages (Hence, they have different update/patching mechanism). Their whole philosophy is you run CoreOS as the base OS for your cluster, and run your applications on top of it packaged as containers. It also provides a bunch of tools for your cluster management and service discovery across containers/applications in your cluster.
PS: the above is a very summarized, focused answer to your question. CoreOS is also much more than what I have mentioned.
I personally found this blog post a bit of a a-ha moment in terms of understanding what docker is vs. CoreOS (and, at the time I was also researching what kubernetes is and how to run it)
PS: the above is a very summarized, focused answer to your question. CoreOS is also much more than what I have mentioned.