Yes, some cats do spray or pee where other animals have urinated in order to replace the old scent with their own. I think that there is some risk to leaving the old rugs down because if the dog peed copiously, the urine would have soaked into the carpet padding and potentially the subflooring. Doing a good thorough carpet cleaning will not get to urine that is that deeply soaked in. Perhaps you could get the seller to agree to remove the carpet and treat the subfloor as part of the purchase price or the drop the price enough for you to hire someone to come in and do it for you.
Of course, not all cats will pee on old animal spots, but I don't think there is a way to tell which cats will and which cats won't. So, I think removing the rugs and treating the subflooring is your safest bet.