I haven't read anything explicitly stating that you can't use Windows but everything that does walk you through what to do seems to involve running a .sh file. Has anybody had any luck compiling any kind of Go for Android, whether it be a library or a full native activity?
No, the all process is tied to Linux (FROM ubuntu:12.04 in the Dockerfile).
That means you would need to have on Windows a Docker-compliant environment (like a boot2docker) in order to launch the
docker run -v $GOPATH/src:/src mobile /bin/bash -c 'cd /src/your/project && ./make.bash'