Nope... light stimulates production, hormones. Beyond that it's up to genetics and nutrition (parasite control). Sometimes predator presence can halt laying.
While having a good rooster can be a benefit for hens in that they find them treats and offer a feeling of security, break up hen fights and such... adding an unknown male could actually delay onset a little... as any added stress *could*.
Most my hens are happier without male influence. But some appreciate it. It has zero baring on my production.
How old is your Cochin?
