How does it deal with the bit reservoir?

I'm guessing that it does not deal with the bit reservior at all. It simply splits the file.

Having done this myself (my Gapkiller program also allows you to split files on frame boundaries), the resulting files will still play even if the bit reservior is split across files. There will be a slight glitch at the boundary because of this, but it will be a less annoying glitch than an actual gap of silence.