There are no batteries that benefit from a complete discharge. Most batteries will be damaged by deep discharge.
The "memory effect" that you mention is a phenomenon that occurs in the chemistry of Nickel-Cadmium (Ni-Cad) batteries. The deep discharge of a Ni-Cad battery may sometimes result in re-conditioning of the battery but more often it simply destroys the battery. There are charging techniques that will eliminate the effect and are more likely to succeed than a deep discharge cycle.