I don't really understand teh question.
You can put a search into a dropdown (not really a good idea from a usability point of view) or you can put a search next the main menu.
I'm not familiar with the menu module you are using.
So from what I see it's not possible to integrate a search.
That has really nothing to do with the gantry template or framework.
I would fake it by just placing the search under the menu-box and add some css to make it look good.
But that's just more of a basic css/design question