If the PSU actually outputs the amps it claims, you should be able to run it.
Calculating the power output on the 12v rails (good PSU's only have one), you should get a max of 348W (The supply has no business being called 430W).
Assuming worst case scenario.
AMD CPU: 125W
Mobo: ~30W (much likely less)
HD7770: tough to find out, but 100W at absolute most (likely much less).
Total Draw on the 12v rail: ~255W
You should be fine, though that supply is fairly low quality. I would advise replacing it as soon as you can to a proper unit.
U sir are a smart cookie :P Thanks for actually explaining to me the reasons instead of the "Derp 800w"