I have having issues getting the USB Serial Converter driver installed because of the "has not passed the Windows Logo Test" error (can't continue due to policy enforcement), so I was wondering if I could pair the BT Shield to my computer and upload a sketch to the Arduino using the bluetooth COM port.
I think I saw some examples of uploading a sketch with a non-shield bluetooth module, but can't find anything for the Seedstudio BT Shield.
Theoretically yes, but without the auto-reset feature. This means you have to push the reset button (of the Arduino board not the BT shield) immediately before starting the upload and you have to have the BT shield preconfigured for that (correct baud rate, pre-paired, etc.).
That's not really a convenient setup. Maybe you change to Duemillanove board, for the FTDI chip you get signed drivers (as far as I know).