Idk, if you are asking for an exception they can probably ask for some sort of proof, just like you can get an accommodation for a disability at work, but HR will want some sort of proof. I would negotiate to provide the proof that reveals the least you want to expose about your health. I work in a public building and we can ask what an animal is trained to do, that is the limit, so a note from a Dr saying this animal is trained to do x for this person might be good.

It should be noted, emotional support is not covered by the ada. So that is more of a no man's land in terms of laws/protections