Yes, unless all of it is called at once, as that would cause a OS crash, meaning the extra ram is simply an over commit. Some OS allow over committing (e.g. Linux), Windows generally doesn't for good reason. This is also why some people claim Linux etc uses less RAM, it doesn't it just over commits what it has.
A 32 bit CPU/OS can only address 2^32 no matter what over committing occurs, and they just make the gamble that you will never 'request' all addressable memory at once.
The fact remains, that a 4GB (2^32) is the maximum.
I'm not sure what you are arguing. You seem to have misunderstood something about memory remapping. It is not about committing memory at the OS level. It is something that happens at the hardware level. Some BIOSes let you enable/disable it.
PAE lets a 32bit OS address more than 4 GB, if you want to go there, but my post about remapping was about using it with 64bit Windows.