Making a widget into a menu item

I tried the adding a widget to the header help page but didn’t get the result I wanted.

I have a menu item called special events. I had the idea to make a custom widget that lists posts from the special event category. I would then place the widget in the menu bar.

Is that possible? The end result would be a widget that gives produces a drop down list appearing on mouse hover. The list would be populated with my posts, and thus always up-to-date.

Not sure if I am just dreaming too big here, but your help would be greatly appreciated if it is possible.