Yes you do need to replace it. What happened is the insulation has melted on one of the windings. That in turn collapses the magnetic field, and creates either less voltage or less amperage. That is if it is on the charging side of the stator. If it is on the Ignition side it will reduce the power to the Ign coil, and produce a weaker spark.
I'm not sure what you mean about the Oil Leak. Can you post a Pict of where it is weeping from? It Always means a seal is going if you see engine oil in the stator housing or Variator housing.