Yes you can.
And actually I think it's a more convenient way comparing to FTP.
- Make sure your Git is set to "commit as-is", so that you can avoid some signature issues.
- Publish your ClickOnce application to a directory in your git repository (you may want another branch for that) with the url of raw on Github as the download/update url. E.g. for repository "xxx", branch "master", directory "clickonce" of user "vilic", the url should be "https://raw.github.com/vilic/xxx/master/clickonce/"
- Commit and push your application.
BTW, you will be able to download exe file and the application is able to check and download update as you are directly using raw.github.com. However, you may not open the xml file from your browser because the MIME type of xml file would be "text/plain". But I think you can try to use Github Pages to build this server, which should response with the right MIME type.