In a sense. For those who don't always grasp the grim ironies of Christian tradition, a saint's dies natalis, or birthday, is in fact the day they died. In the case of Mary Magdalene, the details of whose life are obscure and steeped in legend, we may presume that the date deserves an asterisk -- it was probably chosen later, following some now-forgotten train of monkish logic. But it has been July 22, both East and West, since the AD 900s.
And look: Dr. James Dobson has offered us a little birthday present to help celebrate! For details, read the post above this one.