So when emulating, all I have to do is make sure the address gets updated, correct? I don't have to actually fetch/store that last tile?
You have to go through the motions of fetching on the PPU address bus so that the mapper sees the side effects of the fetch, but you need not actually load the fetched pattern or attribute data into the unpack shifter.
Also, when exactly is the 'x scroll' portion of the $2005/$2006 address reset?
The last two background fetches occur at x=241-247 and x=249-255, the nine bits corresponding to the Y scroll are updated at x=251, and the six bits corresponding to the X tile position are restored at x=257.