Yes, the script requires <a> elements for triggering the sub menus so some modifications would be needed if you would like to use <span>‘s instead.
However, I am not sure there is any serious reason for not using <a>‘s, is there? You could even omit the href attribute if you like (not advisable) and it would still work properly with mouse/touch:
...
<li><a>About</a>
<ul>
...
On the other hand, there is a serious reason for using <a>s inside parent menu items (and not omitting the href as in the above example) – without a link element your parent menu item loses its ability to gain focus and thus the sub menu becomes completely inaccessible via the keyboard (unless you specifically add a tabindex attribute to your <span>‘s but that is still not a perfect replacement for a real link).
