Not in Moodle 2.2.
But in Moodle 2.3 threre will be the ability to drag and drop files directly from your desktop into the file manager element (the blue box) - assuming you are using Firefox, Chrome or IE10.
There was also a 'quick add' button planned for Moodle 2.3 (which does what you want), but I'm not quite sure whether or not that is finished yet.
I was expecting in 2.3 with drag and drop working most places to be able to do it in the file picker, but just found it still has the same Upload a file file picker.
Is it possible / intended to add in a drag and drop box (like in add a resource) at some point?
Test Case: Create an assignment, highlight some text in the description, create link, browse for file, Upload a File, (be nice to be able to drag and drop into this section) - current action: click browse, find file, click ok....
so many steps!
Off OT - Now that files are 'owned' by the resource - in areas like assignments, why not have a box at the bottom that lists the files available for that assignment, and just make a drag and drop box in the assignment settings page? (people can still link if they want... but this would be MUCH faster than click, link, upload, ok etc...