I got a bit further but still don't have it working. I reviewed the VMware-issued whitepaper (the one I linked in my original post) again and the following was in the "Recommendations" section:
When connecting a webcam in a thin or thick client, make sure that both the thin/thick client and the VMware View desktop use the same USB generic video driver "usbvideo.sys".
Having read that, I uninstalled the Logitech camera software and drivers and now have the webcam using Microsoft's generic USB video driver on both the Windows 7 install on my laptop and in the View desktop. But in the video configuration area inside of Lync (which is running inside the View desktop), I see an empty black screen where you would normally see the output from your video camera. In the whitepaper, it mentioned that this exact symtpom might be experienced with webcams connected to zero clients running firmware older than version 3.3. I'm running a thick client though. This whitepaper has given me hope that what I'm trying to accomplish should be feasible, but so far I've not had success. Any help would be greatly appreciated. Thanks!