Given the abundance of non-human casts in kid's cartoons and films, I'd say yes, people can relate to non-human characters.
BUT. Any story where the reader cannot empathize with the cast is going to be a very hard sell. You can tell an interesting story about rocks with googly eyes, so long as they experience relatable emotions and struggles, even on the simplest levels. Likewise, you could have an all-human cast, but if all the characters irrationally and don't adhere to what we understand as normal logic and emotions, it will be very difficult to relate to them. That's not to say you couldn't tell a story about a world with totally alien logic, but there needs to be at least one "window" character that we can identify with and see ourselves in.
You can make a faceless or masked character relatable, but it means going to extra mile to convey emotions through body language and composition. City of Blank comes to mind instantly, as the cast consists of masked characters, and yet they are very expressive through their actions and body language. I mean, Pixar made lamps seem relatable, for goodness sake.
At the core of any character, human or not, there needs to be some element in which we can see ourselves, otherwise it will be very hard to feel connected to the story.