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I assume it would be possible, but have never done it this way myself. It will still require clicking a link in the main menu though, as you can only assign one module to the top page.
By default registered users have access to all areas of the site. What you would want to do is create a custom group, remove the member from the registered members group and assign the member to your custom group,then assign just the access permissions that you want that group to have. If you only give him access to one module that will be the only module link available in the main menu.
Like I said I have never done it this way, so the method may vary slightly. Good luck with your site.
HTH.