Emotional Support Animal in "No Pets" Apartment

Hello, is there anyone with an ESA who was able to purchase a co-op apartment that has a "no pets" policy? What's your experience? There is an apartment in Queens, NY that I really like to purchase but unfortunately, they don't allow pets in the building. I have a cat and he is my ESA. I know that the Fair Housing Laws state that it is a violation if "refusing to waive a 'no pet' policy for tenants that require a service, assistance or emotional support animal." However, I'm still afraid that they will reject my application because of my cat since I heard that the board is not required to tell you the reason they reject you. What are the chances of having my ESA (cat) live with me and my family in a "no pet" co-op apartment? Thank you for your time to read my concern.