Yes! In fact, you should read some of Temple Grandin's books - for example, Animals Make Us Human, Animals in Translation, Thinking in Pictures. Dr. Grandin is an animal scientist and autistic.
I work with dogs with "mental" problems in my work. There is much we still do not understand, and the difficulty with animals is that we cannot communicate via a common language. So, therefore we cannot really know what they are thinking.
We know animals grieve, and they can get depressed and anxious. They can have obsessive compulsive disorder and it is perfectly reasonable to think they can have some of the same other mental conditions.