Technically no. Unless the dog provides a service through work then they are not a service dog. Those are considered companion dogs. A companion animal provides relief from symptoms after an attack such as anxiety. If someone has anxiety or depression a dog can not stop it they can only help emotionally with symptoms.
However, a PTSD dog can be aware of triggers and help steer his owner away from them or help protect others in the event of an outburst etc. A seeing eye dog alerts the owner/handler to danger and helps them navigate through the world. A seizure dog alerts its owner/handler to insets of seizures and some can even call for help and turn the person on their side in the event of a seizure. All of these dogs have a job and typically are not allowed to be played with
while working.
ADA laws were edited in 2011 to strengthen the wording and specifically outline what a service dog vs companion animal is. Under the current law only service dogs are allowed and their owners are protected as long as the dog is well behaved. Any dog that is a danger to the public can be removed service or not.
I posted on here before about an incident I saw at AK a few years ago. I had ran in one day just to take one ride on the safari and to ride EE a few times single rider and wanted to be out of there before lunch. I had the best driver I had ever had on the safari. He was so good and so enthusiastic trying to get us good photo ops and talking about the animals. He was the best driver I had ever had. I made a point of stopping off at guest services that morning as I was leaving the park, to fill out a comment card about how good he was. As I was waiting in line, there was a lady at the desk holding a little, yapping Yorkie. The dog was adorable, but so totally out of control, you couldn't help but laugh. I didn't realize those little things were that strong. It was all the lady could do to hold onto it.
Anyway, she was furious. Apparently she had been kicked out because of the dog's yapping and running at people. She kept insisting it was a service dog and they had no right to ban it from the park. I heard the CM behind the desk, saying that yes service dogs are allowed in the parks, but the owner must have control of them at all times and apparently this little dog had charged yapping at a larger service dog, as well as guests and if she couldn't control him then Disney did have a right to ban him. If the dog hadn't been wriggling and yapping so much at the time, it wouldn't have been so funny, but it was apparent this dog had had no training and very little if any socialization. She had no control over him whatsoever. What' s funny is I then saw them a few days later over at MK and the teenage daughter was carrying the little dog around and he was trying to lunge out of her arms, growling and yapping at people. I know small dogs can be service animals, as well as therapy animals, but no way was that little dog either one. He was too busy misbehaving to concentrate on any job. He was too cute though. He was on a leash, but was being carried both times I saw him and was fighting to get down.
There was no way those people were going to be able to enjoy the parks, with that hyper little bundle of uncontrolled energy. He was obviously just a pet that they were calling a companion dog, so they could bring him to WDW. I feel sorry for whoever was in the room next to them. Both times I saw the dog he was yelping.