Mike ~
Although I don't happen to believe a service dog is necessary for helping an AN patient with balance, hearing and/or sight deficits, that is an individual decision only the patient can make. Most AN patients learn to adjust to their balance deficiencies, SSD (sometimes with a BAHA) and the usually temporary loss of useful sight in one eye. However, there is no 'rule' and if you feel a service dog would help you, then, by all means, try to get one.
I like epodjn's observation that a pet dog can actually serve almost the same purposes as a dedicated service dog, especially when using the dog's acute hearing ability to help the AN patient (and pet owner) know that someone is knocking at the door, the phone is ringing or someone is speaking to them from another room. Employing a pet dog as a walking companion is also useful. Of course, if one doesn't already own a dog, this doesn't apply. Still, acquiring a pet dog that responds well to sound (as most do) might be more practical than trying to purchase (and train) a service dog.
Jim