Does Baron Nashor score when entering and getting played to Baron Pit from his ability?

Yes, playing Baron Nashor to the Baron Pit battlefield token can result in scoring a point for conquering that battlefield, provided you have not already scored that battlefield during the current turn.

Reasoning

1. Entering the Battlefield: Baron Nashor’s ability adds the Baron Pit battlefield token to the board if it is not already present, and Baron Nashor enters that location. By entering the Baron Pit, he establishes control of that location.
2. Conquering: According to Rule 446.1, a player scores through a "Conquer" when they gain control of a battlefield they have not yet scored this turn. Playing a unit directly to an empty battlefield (which the Baron Pit is upon creation) counts as conquering that battlefield.
3. Scoring: Because you are gaining control of a new battlefield that has not been scored yet this turn, you satisfy the requirements for a Conquer. Per Rule 448, when you score, you earn a point (subject to the limitations of the Final Point).

Important Nuances

• Once Per Turn: Per Rule 447, you may only score from a specific battlefield once per turn, regardless of whether it is through Conquer or Hold. If you have already scored the Baron Pit this turn, playing Baron Nashor there will not grant you another point.
• Final Point Restrictions: If you are attempting to score your final point to win the game, Rule 448.1.b.2 applies. You will only score the final point if you have already scored every other battlefield in play this turn. If you have not scored every other battlefield, you will draw a card instead of scoring the point.

Note: I could not fully verify this ruling against the retrieved rules.