this shortens the string from both sides and gives the player the ability to engage/disengage as part of their right-hand playing.
Because of the way intonation works in string instruments (e.g. by fine-tuning the saddle of the bridge on electric guitars/basses), I think that you'd be able to have this set up to work well in a few playing positions, but just as the frets get smaller as you go higher up the neck (because of the way pitch works on a shortened string) I'd expect the intonation to get out of whack in other spots on the neck.
You'd be out of tune if you used both a palm fret and a neck fret at the same time on the same string. But I doubt that you'd ever want to do that. The palm fret only moves 1-3 semitones, which if you're already putting a finger on that string, it's almost always going to be easier to move the finger a fret or three than to use both the palm and the finger.