No... but yes

To load the Run window, you must left double-click the VDT icon within the notification area.

However, in order to make it quicker, you can add your own icon to the notification; left-click the VDT icon within the notification area, choose "Settings" and then "Virtual Desktop Toolbox". Use the "Notification area" tab (third tab) to link an icon to the default desktop and then link a short action ("Left button click" for example) to the Run window (choose "Load the Run window" in the right combo). Go there for more information: http://www.r2d2-software.com/VDT/Tutorial/Default/Page5-6.htm.

But you can use too the "Run..." shortcut that was created in the "Virtual Desktop Toolbox" folder of you Start menu while VDT was installed. You can assign a keyboard hotkey to this shorcut (left click the shorcut and choose the Properties option). Everytime you press the hotkey, the Run window is loaded; the only restrictions is that you cannot create new commands within the integrated library (use the Run window loaded by the VDT icon to do it), but you can use the existing ones (top combo list).