Shotcrete would be an excellent process to repair or overlay your wall. You are correct in saying that it could not only repair but also reinforce and enhance the strength of the wall system. It is important to remove all deteriorated brick and sandblast or water-blast the surface if you are looking for a good bond between the shotcrete and the existing brick. Dowels epoxied or grouted into the existing brick are often used to mechanically tie the shotcrete overlay to the brick wall and also stabilize the new reinforcing steel in the shotcrete overlay.