In my experience the channels are not always totally discrete - there can be a degree of crosstalk, it usually takes some digging through the advanced menus to try and minimise this. A compressor inserted on the voip return keyed from the mix minus voip send effectively mutes the feed from the voip when you're sending to it, similarly a comp on the voip send keyed from the voip return mutes the send when you're receiving signal from the voip end.
As for whether reaper will recognize the channels, does this mean that your video conferencing unit has usb connection? I think it's unlikely to carry audio, best bet is to stick with your sound card. You can definitely generate mix minus with reaper, use the routing matrix view to manage your sends.
If your soundcard has enough inputs and outputs, and you're confident your computer is stable enough, you don't necessarily need the a&h desk, other than maybe as a backup.