This is very similar to the “normal” Docker Machine setup. You should absolutely be able to install Docker on to the VM, and use it like any other service running on the VM: you can run docker commands from a shell on the VM, and anything you e.g.docker run -p 8888:80 you can access from the host at http://172.16.x.x:8888/ where the 172.16.x.x address is the IP address of your VM, and 8888 is the published port number.
You probably won’t be able to run Docker commands directly from the Windows host, and I gather from the forum that native Windows (beta) Docker has some ability to run Windows-based applications in containers, which I presume also won’t work in a Linux environment.