you could, but i think you'd need to find a driver revision that supports both (i've had a case where a new driver dropped support of an older card, so i had to use a previous driver to capture them both)
a better idea is to use dual cards, one nvidia and one amd, so that you can pick the one that the game works with best. this works even better if your monitor has two digital inputs (like DVI + HDMI) so that you can switch it right from the monitor