I just tried putting a P bass neck from a MIM P bass on my American Deluxe Jazz bass. The neck fits, but I couldn't adjust the intonation. If the open string was in tune, the bass was out of tune above the first fret.
The scale length is different, so the 12th fret on the P bass is not halfway between the nut and bridge on the Jazz bass. So to make this work, you will need to move the bridge.
