Yes.  Takes a while.  My hens didn't start laying till 7 months.
Cockerels are so big and ungainly they have difficulty doing the deed successfully.
The offspring will not be true CX.  Though they may provide valuable genetics.  There are a number of CX hen offspring chicks in my culling project, about half got the "size" genes, the other half were typically sized, an all got the dominate white gene.  The few who have aged up some all appear to be relatively late layers, as well.
Most people trying to breed CX to obtain some of the genetics do so by placing the birds on feed restricted diets to slow their growth rates and keep the weight down.  Helps with mortality, but they remain very "brittle" birds.