You can indeed connect your OnDemand account to your Github repositories, as explained in this blog: http://blogs.atlassian.com/2012/02/connect-source-jira-issues-dvcs-bitbucket-github/
However, the Github repository cannot be managed in the same way that an internally hosted SVN repository can be managed and not all the functionality will be available to you because you can only connect your JIRA application and not FishEye/Crucible, (in the event that you are using them).
All the best,
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