LIstbox has drag operation performed with DragDropManager. AllowDrag = True and DragVisual set on DragInitialize. 
RadToolTipService sets ToolTip for element in the ItemTemplate of the ListBox (for example TextBlock).

While tooltip is open , dragging from listbox results in 2 issues:

    - tooltip is not properly closed

    - tooltip cannot be shown anymore on the listboxitems

A possible workaround is to set telerik:DragDropManager.AllowCapturedDrag = True on the element which has RadToolTip.ToolTipContent set on itself.