It is not possible for the dedicated card to process graphics if the monitor is not plugged to its outputs. However, the card should output video on ANY monitor even without the drivers installed. If you are getting a black screen when using the GPU, it might be faulty.
If your problem only occurs with that specific DVI to VGA adapter, you could try another one. Also make sure that you are connecting the DVI adapter to the analog DVI output from the GPU.
