Hi Jim,
There is a connection between the sign-up and the WP users, but currently it’s only to link sign-ups to a user so they can later remove themselves if needed or so you can export the sign-ups and know who was logged in when the sign-up came through. There is also a feature in progress that is expected to be released with the next version of the plugin that will allow your users to see a list of all the tasks they’ve signed up for in one place.
However, I believe you can accomplish what you are looking for if you use a separate plugin in conjunction with Sign-up Sheets. If you use a plugin such as WP-Members it will allow you to restrict the sheets to only be available once the user logs in. Once installed, just make sure to go to Settings > WP-Members and under the “Custom Post Types” section, check the box next to “Sign-up Sheets” which allows you to secure individual Sign-up Sheets to require you user to log in before accessing them.
Let me know if that works for your needs or if not, what changes you would like to see instead.
Thanks!