You can drag and drop into the recycling bin widget IF AND ONLY IF "Lock Dragging" is OFF in your settings, AND you can also drag a shortcut onto the Internet Explorer widget to launch the link, for example, so the mechanism for this kind of operation must exist, but there seems to be no way to precisely do what you ask.

Perhaps if there were two "lock dragging" settings. One for on/off "Lock Dragging of Shortcuts" so you could lock the layout and items on your dock. And then a second for "Item Dragging and Dropping" On/Off for items that would have active operations if dropped onto a shortcut with a default behaviour, like copying files into a folder shortcut, links to IE, trash to the recycle bin, etc. etc.
I assume it would operation just like shortcut on the desktop do (for example, you can copy a file from the desktop into a folder shortcut on the desktop in Vista and the file will be copied into the target folder), so it doesn't see like a huge chore to link to that interoperability, yes/now?