Search bar logic is described here:
https://www.lansweeper.com/knowledgebase/searching-through-assets-with-the-web-console-search-bar/
So, there seems to be no plan to include the AD description field into the search bar index.
For me it would also be a solution to have Lansweeper copy the AD description field contents into the Asset description field during scanning/when receiving AD information - if not locked/inhibited explicitly using the padlock symbol on that asset description field.