It seems that
"make noise: emit a noise (could be any noise such as one from music, TV, people talking, …)" Source
"make a noise (about something): (informal) to complain loudly (talking about human only)" Source
"make noises (about something) (informal):
- to talk in an indirect way about something that you think you might do
The company has been making noises about closing several factories.
- to complain about something" Source
But I am not sure if my research is right or not?
Best Answer
Noise can be countable (refering to individual sounds that are noises) or non-countable (refering to a stream of sound with qualities like noise). So make a noise does not automatically mean "complain" and make noise can mean this too.
Make [a/some] noise about X can be figuratively used to mean "doing something to gain attention about X" but I'm not sure that association is strong enough to really be an "official" well-known saying, but certainly a strong implication.