Yes. With the most recent version of JAWS, there is an additional step users must take for the software to read mouseover annotations (Tooltips are mouseover annotations). This site, http://www.freedomscientific.com/downloads/jaws/JAWS13-previous-enhancements.asp, lists enhancements and improvements with JAWS 13.
One section reads "Added long Keyboard Help messages for the list of on MouseOvers (INSERT+WINDOWS KEY+SEMICOLON), next clickable element (SLASH), prior clickable element (SHIFT+SLASH), and list of clickable elements (INSERT+CTRL+SLASH) keystrokes. To hear the long description for a command, press the keystroke twice quickly."
By following the steps for mouseovers above, your students will be able to hear the Tooltips read to them.