Video card issue a symptom of power problem?

So I have the HD 4870 card that sounds like it is running at max speed pretty much all the time even on 10 year old games.

I am getting a new PSU to fix a different problem and I was wondering if people thought this fix might kill two birds with one stone or not.

So the direct question would be:

Can a bad PSU cause a video card to feel like it needs to run at max all the time?

I wouldn't "think" the two things would be related, but I do know that failing PSUs can have effects that are quite numerous and show up in places that people wouldn't normally think about.

How likely do you guys think it is that a new PSU will *calm down* my video card when I am doing the same exact things I am already doing?

I recognize that my video card is beastly in general, but it just seems like it should be at least slightly less beastly sometimes.

I figure the new PSU probably won't do much to affect this problem, but I was just wondering if anyone has seen an instance of a new PSU causing a change in video card operations.

I am going to find out the answer in 3 - 7 days anyway, but if there is no chance for the video card to act different after I get the new PSU I could just get an aftermarket cooler now rather than waiting till then and finding out it didn't have an effect.