Edit: This no longer works. Organizations now provide the same curl result as users.
This is a bit of a hack, but it seems to work.
[~]$ curl -sI "https://hub.docker.com/u/google/" | grep "^Location: " > /dev/null && echo "Organization" || echo "User"
Organization
[~]$ curl -sI "https://hub.docker.com/u/docker/" | grep "^Location: " > /dev/null && echo "Organization" || echo "User"
Organization
[~]$ curl -sI "https://hub.docker.com/u/dfarrell07/" | grep "^Location: " > /dev/null && echo "Organization" || echo "User"
User
[~]$ curl -sI "https://hub.docker.com/u/davetucker/" | grep "^Location: " > /dev/null && echo "Organization" || echo "User"
User