Well yeah that isn't optimal but I doubt the PC will run any faster. If you were reaching thermal throttling temperatures with that paste you probably will hit them even after replacing the paste. Do you have a program like HWinfo that could monitor the temps and log if you're hitting the throttle limit?
That is a processor with some very dried-out looking thermal compound on it. I had to deal with a similar situation today on a machine I was working on.
I bought a GPU off ebay that had thermal paste like this, the pads were also worn as fuck. New thermal paste, new pads, and it went from shutting off every 5 mins / ridiculously slow speed to good as new. Amazing what a difference just fresh paste made