It's completely possible and I think it's possible to make such a device with 100% compatibility for the NES. Honestly the GAR works amazingly well for the vast majority of games, it just can't handle really complicated mappers, especially ones' with more than 8KiB WRAM. The worst problem with it is the botched controller logic which makes it sometimes save/load states when you don't want it to, just because of how some games read in the controller...
How it saves/restores PPU registers is easy, it itself has local PPU registers mapped to the same addresses as the real ones, but the local ones have readable ports mapped somewhere else.
How the GAR exactly works with mappers however I don't think is known, but I suspect it can store a certain number of $4018-FFFF writes in a buffer which intelligently purges old values (or a FIFO maybe?), then writes the values back while restoring the game. To figure it out further someone'd need to test games with specific mappers and see what stuff fails. I think it will even work with Battletoads and other crazy timing games because it doesn't steal CPU time at all.
Back on topic: Yeah, I don't like Neoflash either since:
-They are the same as the giant 3rd party factory Xinga (
www.xinga.com)
-They have something to do with practically all Famiclones/MDclones/SFClones ever
-Their crappy controllers are similar enough to authentic controllers for many people to confuse them, which is why it's much harder to find authentic brand new SNES controllers these days...
-Their prices can be very overinflated since they're based on whatever people will pay, not on part value + fixed markup, the only item I've bought of theirs is their Neo Geo MVS adapter which is certainly marked up 1333% on <$15 of parts.
-They appear to enlist stupid customers to do their GUI coding work for them, I guess in exchange for the product they helped create...
-They've been proven to use homebrew source without permission/knowledge of the authors.
-They sponsor homebrew contests as a legal cover, which is annoying since undoubtedly they're giant warez profiteers.
-Lastly Neo NES is most likely based on the PowerPak