yes, dogs can be mentally ill, including ADD. Puppies raised on omega-3 deficient diets (any dry kibble diet that is not supplemented) tend to exhibit ADD-like traits due to abnormal brain development. Also some younger dogs kind of act like they have ADD but they grow out of it; we joke they don’t get their brains until sometime after age 3. Also many people never teach their dogs the concept of “self control” and these dogs may act very ADD-like as well.
However, if your dog is just not paying attention to you that can easily just be a lack of training on your part- you have to spend time and effort convincing your dog that you’re worth paying attention to. One common mistake people use with food-motivated dogs is they bribe them- the dog ignores them, so they show the dog some food, and now the dog pays attention to them. However, what they just did was reward the dog for ignoring them, and taught the dog that the way to get food was to ignore them, and also taught the dog that there’s no point in paying attention unless food is highly visible. Food is an excellent tool but it’s easy to mis-use. You don’t show the dog the food until the dog does something worth rewarding. If you want to reward attention, wait for that split-second glance towards you and THEN whip out the food.