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.
"Twenty years from now you will be more disappointed by the things that you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover." -- Mark Twain