Will this PSU properly support my system's power needs?

That's a really cheap power supply:
"Specs:
+12v1 = 15A, +12v2=7A, +5v=28A, -12v=0.5A, +3.3v=26A,+5Vsb=2.0A
230v 50~60Hz Input Voltage."

Compare the to this 500 watter:
Antec 500 watt BASIQ
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

A 4850 needs about 10 - 12 amps and the CPU will need 8 - 10 amps. That's 18 - 22 amps without the rest of your system.

Get a better PSU.

I agree. You want a high quality PSU, and that certainly isn't one. Get any 500W+ unit from Corsair, Antec, SeaSonic, Silverstone or a 600W+ from OCZ. I say a larger unit from OCZ because they're very cheap, but don't have the highest quality in the lower wattage ranges.

Also, you may want to consider getting a larger unit (like a 650W one) to keep your options open in terms of upgrades. Also, a larger, high quality unit could easily be transferred to a new build.