No, it can do glorified bank-switching. That's not an increase in address space, it's a hack that assumes applications will still keep their memory usage to no more than 2-3GB.
Its not bank switching, its the MMU mapping the 32bit virtual address space of each process to a much larger physical address space. You are right that each process is still limited to 32 bits of virtual address space but bank switching has nothing to do with it.
Having extra hardware to help speed it up doesn't stop it from being bank switching. That is its essential nature, it doesn't matter how heavy the lipstick is.
By that same logic, all of paged memory management is bank switching. I might also point out that current x86 CPUs map 64-bit addresses into 43-bit physical addresses using pages. Is that reverse-bank switching?
It's purely coincidental if your CPU was designed to map N-bit virtual-space pointers into N-bit physical-space pointers. It's much more common, both now and historically, to map from N-bit to M-bit. There is no hack here.
Its worth mentioning also that x86 64bit CPUs still use PAE, in fact they have to, its mandatory in long mode ("real 64 bit mode"). Additionally the version of PAE used in 64 bit mode is an extension of the original 32 bit PAE, adding an extra directory layer to support up to 52 bits of physical address space. Although i don't think any processor has implemented more than 48bits of address space so far.
Having extra hardware to help speed it up doesn't stop it from being bank switching. That is its essential nature, it doesn't matter how heavy the lipstick is.
