Not really. You have to slow the clock speed down when you add a core, which is what impacts gaming performance. This isn't a huge issue when you get a higher end CPU, as they've improved the speeds and the cache on the processors, which makes up for the lower speed from the additional core. However, if you buy a cheap quad core, they can't afford to make it faster, so you get a lower speed, which is all that really matters for gaming.
The reason dual cores are better than a single core despite being slower is that when games used one core, the second core was able to offload the extra processes running in the background to the second core. However, games started using tow cores. So the third core takes on the extra processes. Most games haven't moved past using two cores, and isn't likely to do that for a while still. That makes triple core CPUs optimal.
There are some games that need quad cores to run at optimum speeds. For example, GTA IV really loves quad cores, but that's really about the only major one.
The problem with the processor is that you spend a good $100 on it instead of the $75 on the X3. That's a lot of quality you lose for getting nothing in return. In addition, the X3 can unlock a fourth core, turning it into a cheaper quad. Also, the CPU overclocks amazingly. Those factors mean you can get a faster quad for less, if you get lucky.
Of course, many people actually find the speed loss from unlocking the fourth core (and sacrificing some overclocking ability) actually hurts the gaming performance. So many people unlock the core for performance and then only end up undoing it to get better performance.
The case matters a lot actually. Without a good case with good airflow, parts will overheat, causing the computer to have problems not only in running, but also in longevity. Also, a good case is the base for any build. It protects the parts from everything. Cases aren't expensive either, so there is no reason to not get a good one.