It will run faster, alright. But, Photoshop is a RAM eater shark! Even if you set the scratch disk (page file) in another drive(s), with max. RAM, the longer you work with it, the slower it becomes.
Here's a program which takes advantage of (at least) dual-core CPUs; it's - partially - multithreaded.
I believe the reason Photoshop becomes gradually slower, when working for 'long' periods with it, it's because it not only uses RAM "statically" (i.e., load/stores data from/into memory on a linear basis) but, also, "dynamically" (i.e., it is constantly loading/storing the actions previously performed from/into memory). I don't really know if it works this way... but seems to. Try this simple operation: convert an image from CMYK to RGB and vice-versa, a number of times...