I think that while he may not respond directly to any communication from you his office will make a note that you wrote/called about a specific issue and if enough people call/write about the same issue then they will start to take notice that there is something that needs to be addressed.
No, I do not believe that if I contact Bill De Blasio, I will get a response or make a difference, because he already has decided his agenda. De Blasio is very busy, and can't possibly have time to respond to every email that he receives. If you send him an email, you will receive a form letter for the issue that you asked about.
If I contacted Bill de Blasio I would not get any such response. He is the mayor of the largest city in America so he would say he has no time to speak to me. He is a typical politician and he would think he is too important to speak to me.
It does not seem like representatives actually represent us anymore. Part of the reason is that there are too many special interests and politicians do whatever it takes to keep their jobs. Another reason is just the sheer population. They can't possibly keep up with everyone passing along an inquiry.
As a resident of the Midwest I have to say that I do not think Bill De Blasio cares one bit what I think. Nor do I think I would get a response or make a difference, so to speak. Bill De Blasio is only the mayor of New York. Yes, the population is large there, but not all Americans are from New York City.