Yes, dither before splitting. If you split and then dither, you'll get files that aren't necessarily cut on sector boundaries.
that might be true
if he was resampling, because you'll now have a different number of samples in each song, and each song
might not be cut on sector boundaries.
however, if recording at 24 / 44.1, if he splits the files, and then dithers down to 16 bit (without resampling), there are still the same number of samples in each file, no resampling has occurred, and the files will still be split on CD sector boundaries (assuming that they were to begin with, and with CD Wave, that's a good assumption).
All that said, I would recommend dithering before splitting the files as well, simply from a work-flow standpoint. it's simpler to dither first (along with any other edits/volume changes, etc), and then split the large file into individual songs last.