My wife and daughter keep three or four chickens in the back yard of our home for pets. They have free run of the yard and procuce eggs for free. Another benefit is that they eat weed sprouts and fertalize the yard. So it's a win, win, situation. The problem is that by the time that a new recruit is old enough to start showing signs that it is a rooster and not a hen they have already named it and become attached to it. Then it starts crowing in the morning and disturbing the neighbors and soon it is necessary to get rid of it.

I was wondering if castrating a rooster would remove it's  desire to crow in the early morning.

Capons won't crow.
Shoot, shovel and shut up might be easier than caponizing.

As a general rule a rooster that has been castrated will not "crow" in the morning.

But it's not because of being castrated.................
It's because their too busy trying to peck your eye's out for cutting their man jewels off!!!

Won't that have a negative effect on the production of eggs?

Quoted: Won't that have a negative effect on the production of eggs?

Not really. Hens lay eggs regardless of a  a rooster being around or not.