"Bitness" of a CPU almost always refers to memory addressing.

Now you could build a weird CPU that has "more memory" than it has addressable width (the 8086 is kind of like this with segmentation and 8/16 bit) but if your CPU is 64 bit you're likely not to use anything less than 64 bit math in general (though you can get some tricks with multiple adds of 32 bit numbers packed).

But a 32 bit CPU can do all sorts of things with larger numbers, it's just that moving them around may be more time-consuming. After all, that's basically what MMX and friends are.