Flowers are not chickens

But...you may be on to something there -- after the second year, high production breeds tend to burn out, have reproductive (egg laying) problems and sometimes die.
When you are saying "don't do their best in the
reproduction department the first year" are you meaning in producing hatching eggs or just egg production in general?
Egg productivity is going to be "best" in that first year. After molt, guidelines would say expect around a 20% reduction in production each year thereafter. So....
A female chicken would be considered "sexually mature" when she starts laying eggs - meaning she is ovulating (laying eggs/has reproductive capabilities). IF she were being mated by a sexually mature cockerel (one old enough to produce sperm) - her eggs would be fertile. While not ideal to hatch out "pullet eggs" until the size of the eggs are bigger (say 1-2 months after onset of laying) - it's very possible that you can still hatch chicks.