Maybe. Mine did (well not completely stop but way decreased) It might be just coincidence, I can't tell because these are my first chickens but I read this https://www.backyardchickens.com/articles/the-egg-song-it’s-not-about-the-egg-it’s-an-escort-call.74386/
And I know chickens sometimes see people as their rooster. So, I "escorted" them when they did their egg song. Obviously not every time, but fairly often for a while, and tried to communicate that a little egg song is a good thing.
It seems to have worked. They do still an egg song but nothing like they did for awhile - in volume or duration.
I've also read on here about other people's chickens that were very loud as they started laying but mellowed with age... without any intervention.