Yes, if there's a possibility of a 4th person, it's best to include them when making the original reservation.
Whether you can add a 4th at a later time depends on several things:
1) is there space in the room? (can't put 4 people in a 3 person room)
2) is there space in the lifeboat assigned to that room? (Since there are more beds than lifeboat seats onboard, it's possible that a room can have another - unfilled - bed, but the lifeboat is full)
3) is there space in the appropriate kid's club? (if applicable)
The cost for an additional guest is what the going rate is at the time you book them, not the cost for same guest had they been included in the original reservation.