Sorry, a query is just a window in the application, and you can't run one without the other. So the answer is no.
Time to swallow the pill, maybe, and switch to either Access own 'data access pages' or something like a php-database combination on a webserver. That way it's all web-based and just a favorite and a tab in the browser. No clutter in the taskbar at all.
Kees
Is there a way to link a query from Access to the desktop that, when clicked, will only open the query and not the database? We've tried right click>>create shortcut>>Browse>>Desktop, but it opens the query and the database. It's just clutter on our service shop computers that have many windows and apps open at once!

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic