The service animals covered by ADA law are those that have been trained to perform specific tasks for people with disabilities. That does not include emotional support animals who are there because it comforts the owner to have the animal's company. There are psychiatric support animals that have been trained to anticipate a panic attack (for example) and take actions to calm the owner, but that is not the same as an untrained emotional support animal. Most airline employees will not question whether an emotional support animal has been trained for its role.

Here is information from the ADA website:

http://www.ada.gov/regs2010/service_animal_qa.html