I don't know if it would work fine. Which is why I recommended a power supply upgrade.
How many amps do you have on the 12V rail(s) of that power supply?
Probably not very many, especially if it doesn't have PCI-E connectors. I'd guess 19A on 1 rail. But that's just a guess.
I was wrong....From an Amazon review of a CyberPower system
It's an Xtreme Gear XG-P500 rated at 500w, with dual 12v rails. Significantly, each 12v rail in the power supply is only good for 14 amps, though.