The Athlon is rated for about 100W and the 7970 will pull about 250W all from the 12V rail, thats 350W from a 12V rail that is only rated for 336W. It might do it for a little while, but you are going to quickly kill that PSU and even good units can die catastrophically.
Drop down to a 7950 and actually get a PSU meant to run a graphics card of that size.