Dragging the notes to Omnifocus does nothing. And you can't copy the note to the clipboard. You CAN copy the contents of the note, but not the note itself.
What I would absolutely love to have is some sort of linking between Omnifocus and Evernote. Drag the note to Omnifocus, create a link. Click the link and pull the info up from Evernote.
Unfortunately, I really think the burden here is on Evernote to cooperate better with other apps. External linking seems quite common among other Mac apps (e.g. Apple Mail, Address Book, Yojimbo, DevonThink, Journler, etc.). I'd expect Evernote to be able to do the same. In fact, I'd personally be hesitant to use an app missing this important functionality.
Have you tried making a feature request with the Evernote developers?