The short answer is no. As long as your animal is well-behaved, there should be no problems with your ESA letter. The ESA letter is based on the owner's needs, and not dependent on any specific training for the animal. However, even with an ESA letter, the owner is still responsible if their animal causes damage to property or harm to others. In most cases, people who are seeking an ESA letter have well behaved animals, so there are rarely issues that cause people to call the letter into question.