No, power can make things fail. Overvolting can cause overheating, undervolting can cause current draw that will kill things. But on the whole, with power it either works or it doesn't. You would see a lot of errors and symptoms if there were bad power. But it's not like the system would just be slower. Try measuring the current with a voltmeter and you'll see if you are exceeding your PSU. You can also measure the load voltages on the lines, or look for line noise. Those types of things require tools though and are best left to professionals.
Short answer: No, PSU can not possibly bottleneck your performance. But it can cause errors that will effect performance (though these should be obvious, and you'd likely see BSOD).
If you post your hardware we can offer more advice. =)
