Assuming decent quality (doubtful with that brand), the PSU has enough capacity to run your system.
I have a similar system in terms of power demand: (GA-EP45-UD3P | Q9550 OC'd to 3.6 GHz (425 MHz X 8.5) | 4 GB RAM | 3 HD's | GTX260 (close to same power requirements as a 4870)). It pulls 300 watts from my TX750 PSU. So you should be all right.
Without some fairly expensive equipment, it is almost impossible to load test a PSU at home.