The address space is a part of it however. Most forms of XP are 32bit. This means the OS can handle up to 4GBs. In hex values, this ranges from 000000 to FFFFFF. (I think thats right.) Counting backwards the OS will start using the FFFFFF address on back to store info including whats in the GPU frame buffer, HDD cache, etc. So while the memories are different, the space is still used.
There is some disagreement on this forum as to how much. Most will tell you the entire 1GB is duped. I don't believe this is the case. The OS will reserve some space, but not the full 1GB. It doesn't care about AA/AF being applied which does take memory space on the card. I'm not sure how much the OS "remembers", but I don't think its 1GB.