Sounds entirely do-able Matt. The extended desktop (dual monitor) setup should work fine.
You might need to watch as some webcam software switches off if not the "active" windows program.
I would recommend "YawCam" - its totally free, got loads of nice features, and most importantly, you can set it to transmit continunally, or even go into PIP (picture in picture) mode if it is overlaid over another Windows program.
Think the website for it is:
http://www.yawcam.com/