If you have the right sort of fish, sure!
For example, some loaches and gouramies can make a clicking noise and corydoras croak.
Many seafish can make a grunting noise.
Although noise is always made with fins, scales, swim bladder vibration or gills rasping. They can not make vocal noises.
The noises fish make are mainly used for showing off to Mrs fish or aggression. The main communication made is visual, smell/taste and pressure on the lateral line.