I've done this mod several times for customers. It would be great is you could add a hook so it would not have to be a custom mod.
Please add a backend hook at the end of the order_search_form 'simple search' list so we can add other fields to a simple search.
{hook name="orders:simple_search"}{/hood}
While you're in there, you could add the 'order_id' to the simple search as well. Many times an admin is doing paperwork and needs to quickly look up an order by order_id. Additionally, if the results of a simple search or an advanced search results in one order, have it redirect to the orders.details page rather than the orders.manage page. Reduces the number of clicks to get to where you want to be.