You can only run 64-bit applications on 64-bit operating systems. There are some special exceptions but Dolphin is not one of them.
I don't know if that was a mistake, but you can run 32-bit apps on x64/64-bit operating systems such as Windows XP x64 and Vista x64 using the Wow64 emulation layer.
32-bit applications and games run just as good on Vista/XP x64 as they would on a normal 32-bit Windows install..
However, 32-bit Windows will only be able to run 32-bit applications and games.
In response to the op, the "32" in JIT32 means that you are running the 32-bit build of Dolphin with the 32-bit JIT core recompiler, which is slightly slower than the 64-bit builds of Dolphin.
If you were running the 64-bit build of Dolphin, it would say JIT64. It has nothing to do with how many cores your processor has.