That I'm not sure, you'd haveto play around with it. But my guess would be that as soon as someone clicks on your drag handle then the element they clicked on is cloned and put right under the mouse cursor.
Problem with that is if I start to drag then stop, I'd have 2 elements in the same error overlapping eachother. And if I kept doing that, it could get really messy.
You'd probably be better off using an iconic button to let the user click the edit button, have a modeless window pop-up in the center, let them drag it in there, and when they save it, update the side and close the pop-up. Not as elegant, but prevents confusion.