Yes it does. It grows three times immediately, then whenever you shield, attack (Minus Up-B or some air attacks) or even move or turn around, the mushroom will make contact with Charizard and cause it to grow more. What looks like the way to disable the mushroom, its AAA attack, becomes impossible to do as after the first A, the mushroom will contact it and cause it to grow and cancel out the chain. This means the mushroom will never go away. So yeah. Charizard will still continue to grow.
Though in this case, it really does make Charizard a Dragon GOD. =3