No, there is no way to do that with the existing Sign-up Sheets plugin.
That would require quite a bit of extra programming and new admin/user interfaces, plus new database tables & fields to store that information, new report generation, etc…
In short, not something that would be quick or easy to implement.
Feel free to add that to the feature requests section, but that would most likely have to be either a custom programming job for hire, or developed as a separate paid extension (which would not be worth the time if only one or 2 people are interested).
For now, you would just have to do that via email and phone communications, and track things with a spreadsheet or any other system you want to use. Not something we needed for our school’s volunteer events, and so it’s not something that I programmed into the plugin.