Invisible? Not literally, of course. But, yes, invisible in that the public is unaware of your dog's presence unless they walk past you. No matter where you go with your service dog, he should be well mannered, focused on and in sync with you. People who observe you leaving a restaurant should be overheard saying "I didn't even know there was a dog in here." In this video, 17-year-old Annie grocery shops with her 10-month-old Diabetic Alert Dog, Pacey. Note where he is sitting and his demeanor. He is quietly waiting (and watching) his handler.
Young handler. Young dog. Great job!