Hard to say if turtles do but animals, more likely mammals having larger brains and a higher thought process, yes. I've seen dogs, cats, deer, as the previous answer given, horses and even came across a case that had ferrets reacting to an unseen entity. So absolutely they can. Their senses are way more sensitive than ours, sensing storms, earthquakes, danger and even a good or bad person.
-J (via Sinister Sightings Paranormal Society)