But that suggests if you have 2 cores or a single core processor, that performance differences compared to a quad is negligible. And that may or may not be the case.
So for everyone above who said "no". I respectfully disagree and say the answer is, "it depends". It depends on where you are starting from. That is, for example, specifically which dual core and which quad core - and which game too.
So for Vineet Reddy, since you did not specify in your opening post the specific CPUs, how many cores, their speeds and which games, so the answer is, "Maybe, maybe not. It depends". If comparing 1 or 2 cores to a quad core CPU, then yes, it could make a difference. If comparing a quad to a 6 or 8 core, probably not.
To further add to the muddiness of this, it depends on the game too. And not just the game, but the age of the game (many newer games take advantage of more cores).
And finally, (if not most importantly), it depends on the speeds of the processors in question.
So bottom line is the OP's question is too vague and generalized for a yes or no answer. So instead, the correct answer is, "it depends".