2nd dept. admission (NY) - letter to expedite does it do anything?

Sorry I know that these kinds of questions get annoying, but I don’t have anyone else to ask. I submitted my apt about two weeks ago and included a letter to expedite from my employer (public defender). I emailed today to follow up and see if they needed anything else, but they told me they haven’t finished reviewing my application. They said they cant tell me how long it’s gonna take. Got the impression that they were telling me not to follow up lol. Do letters to expedite help or will this take forever?