Yeah, but it wouldn't be in the traditional position for a p pickup, which is between the Jazz pickup postions.
well, the p pickup is not actually between the J pickup positions. It is a split pickup though, so there is some filling to be done to makeup for half the pickup anyway. You would fill the Jazz rout and make a new rout for the P pickup. This is what a good luthier would do.
The P-bass pickup is actually pretty close to the neck route for a J bass, it is not in the in between position.
This does come back to the 'carvin should offer a p-pickup' scenario though. If they offered it it wouldn't matter.