Just a technical note....
Yes, this is possible, but whoever thought of it should be shot for crimes against sanity. And then given a posthumous medal for ingenuity.
The TV card has its own processor, with its own set of RISC instructions and usually its own RAM too.
The graphics card is also active and outputting its video output (the VGA connector).
Therefore if you create an overlay buffer on the Voodoo and don't switch out the Voodoo when you run your game, the Voodoo won't lose its frame buffer because the game will just use the native chipset which won't affect it at all. The TV card will continue running its own little program from its own little RAM buffer, dumping the video input straight to the RAM on the graphics card because the TV card is busmaster and can DMA straight to the graphics card without going via the rest of the machine (which is of course busy running Gods or whatever by now). As the Voodoo is still active, the net result is the TV input running on the VGA output of the Voodoo, which in this case is the Amiga's composite out, probably.
Essentially you have a very specialised computer just consisting of a TV card and a graphics card, running completely autonomously. That's why you must tell WhdLoad not to reset the Voodoo, else it'll close the output or release the Overlay buffer.
