The answer to that question is Yes and No.
Q#1. Can I run an ATI All in Wonder Radeon PCI in the same system??
A#1 Yes you can but for the multimedia functions of the card to function you must set it as your primary vid card and by the way, these multimedia functions can only be displayed on primary monitor.
Q#2. That should give me the best of all worlds or would I just be creating capturing conflicts?
A#2. No it will not give you the best of both worlds cause what used to be your primary super speedy card will now be your secondary vid card with loss of gaming functions. Games are loaded and played on primary card which now would be your ATI card.
You could get a different PCI card for secondary monitor and add the ATI TV Wonder PCI card for it's multimedia capabilities (that is if you have the available PCI slots) this SHOULD give you the best of both worlds AND give you the option to display the multimedia functions on primary monitor OR secondary monitor. (the last part concerning displaying the multimedia functions on primary monitor OR secondary monitor am not sure about so you may want to research that further).
Good luck.