Yes a GTX 570 will work in that board, but it will be severely bottle necked by any CPU the board can accept. I believe that board will only accept Pentium 4 single core processors. And the RAM is only DDR2 533MHZ max. Extremely slow.
As far as the 600W PSU, it all depends on the quality of the PSU. We need make/model of the unit to see if it is a "real" 600W.