You can create an action which calls the script via the Insert Menu Item
command, then assign an F-key shortcut to the action.
However, Illustrator fails to retain script designations in actions when you quit the application (long standing bug) Fixed now. So, this means every time you launch AI you have to reset the action to see the script. However, Illustrator fails to retain script designations in actions when you quit the application (long standing bug). So, this means every time you launch AI you have to reset the action to see the script.