A quad core processor is only 1 physical cpu. For intel quad core processors, the cpu consists of 2 dies, with 2 cores on each die (not sure if this has changed, it's been a while since I read up on it). Whereas with AMD quad core processors all 4 cores are integrated onto a single die. This is meant to improve the the communication between cores...
Windows 7 home basic only supports up to 8GB RAM, Home Premium supports up to 16GB RAM, Professional, Enterprise and Ultimate support up to 192GB RAM, these figures are based on the 64-bit versions. Hope this answers your question.
For intel quad core processors, the cpu consists of 2 dies, with 2 cores on each die (not sure if this has changed, it's been a while since I read up on it).
That's true of some of the older "Core" processors, but not of the new Core i3/i5/i7... processors. All of those newer processors use a single die with 2 or 4 CPUs and lots of cache integrated onto it.
I'm getting an i7, so will this mean there will be some performance boost from ultimate?
No. What you get with Ultimate is some more features (BitLocker drive encryption is an example), but the core services that run your programs are identical in all the versions - so programs really won't run any faster in one version vs. the other.
The only exception to that might be if you're low on memory then Ultimate might conceivably run a bit slower because the extra features use a bit more memory and that might force more paging to disk. But if you have enough memory then it really isn't going to make any noticeable difference.