No, annealing does not return brass to "almost new" condition. Primer pocket looseness, damage to extraction, inherent fire-forming changes to the brass, etc is taking effect on the brass. It only softens neck hardness of fired brass. How the brass is annealed will determine if neck hardness returns to its original softness. If you over anneal, damage can occur to the brass. If you under anneal, it may not return to correct softness.
There are multiple factors happening to brass each firing that annealing does not address so a correlation to annealing and extending brass life will not be a complete discussion without taking all of the other factors into the equation.