This is a terrible idea, but can be fixed. The problem is that it makes the dotfiles public. These are files that are normally private, and so it would be easy to forget that you've exposed them and do something like add a shell alias or vim macro that includes sensitive information.

Replace Github with Dropbox and you'll be a lot safer. You can still use Git to manage revisions. That part of the idea was fine. Just don't have the remote repository on a public service unless you are sure you can avoid errors.