Thanks for the comments Rochelle.
Hour tracking is not a current feature of the plugin, so you would have to do that manually.
Of course, it is possible to track hours, but that would take quite a bit of custom programming to add that feature. If your school has the budget, I could be hired to develop that for you. Otherwise, this Feature Request area was the right place to post that as this is where I will check for the most requested features if/when I have the chance to work on new extensions for this plugin.
Also, please note that the volunteer sign-up sheets plugin I posted on WordPress.org is completely open source, and already has lots of hooks in place to allow other developers to create extensions for it. So, if you have someone in your organization that can do some programming, they could probably create some kind of add-on to track hours, or even directly modify the plugin for your own use. In addition to myself, there are plenty of other developers out there that you could also hire to help you, if you have the budget.