Applying for a new apartment with an emotional support animal?

I have an emotional support animal (a cat), and am currently looking for a new apartment. I know ESAs are covered under the FHA such that a landlord is required to make reasonable accommodations, including allowing them in "no pets" apartments. Even so, I'm concerned about being rejected from apartments (however illegally) because of my cat if I disclose it on the rental application. When an application asks if I have any pets, do I have to say yes, even though technically it is not a "pet"? Or can I wait until after my application is accepted to present documentation to the landlord?