A Pentium 4 is a single core processor and uses the old netburst architecture so yes the Quad core would outperform it. An Intel Core 2 Quad Q6600 is really two Core 2 Duos (dual cores) in one chip. Theoretically, it should be twice as fast, but that's not entirely the case. The reason being software. Most software is either made for single core CPUs or dual cores, which means quad cores are not fully taken advantage of and not used to their full capacity. The best example of this is in games where a equally or higher clocked dual core will often outperform the quad.
And to answer your question about whether a quad core running at 2.4Ghz equals 4x2.4. The answer is no. Those ebay listings you see with quad core 9.6GHz CPUs are false. Inside a Q6600 which is the best selling quad core processor, there are four cores running at 2.4GHz. You cannot add up these speeds, it simply doesn't work like that.
If you are doing a lot of video/audio editing and encoding then go for a quad core as these are very CPU (central processing unit/processor) intensive tasks and many of them are multi threaded which means they can use quad core CPUs to their full effectiveness. If you are gaming, then a dual core CPU is better. If the PC is onyl going to be used for surfing the web, word processing etc then a single core CPU is sufficient. I hope this helps you. If you have any other questions then don't hesitate to ask and I'll do my best to answer them.