No, a beak bit won't stop a rooster from crowing.
A lot of people make their rooster a small night house that he can sleep in. The night house should usually have thick, insulated or padded walls to muffle or quieten the sound. The idea is to make the rooster quieter for you and your neighbours by blocking the noise. It won't stop the crowing, but it will be a lot less noisy. Usually people put the rooster in the night house when it gets dark and then let him out again in the morning (maybe about 8:30am). Usually that provides a very good solution for a crowing rooster living in a city
If you do a search for rooster night houses or night boxes you should find some examples
There are a range of ideas mentioned in these threads:viewtopic.php?t=6738viewtopic.php?t=5872viewtopic.php?t=7955606&start=0
If you decide to make a night house you could perhaps tell your neighbours what you are trying to do and it might make them happier if they know that you are doing your best to keep him quiet