Brick cleaner is normally an acid which would attack morter/cement based stains but is less effective against organic soil or atmospheric based soiling.
Why use a corrosive and ecspensive chemical if it not needed?
Plus if it did help the Pro power washers would be using it but I don't know any that do, your machine has the power to do the job with any additional help
BUT,!! To be honest I have'nt tried it, it might help..... have a test it might make the job easier