On some level, yes. We are all 99% the same genetically speaking, and so our bodies are communicating non-verbally even when we aren't consciously talking, looking, or directing action towards others. For example, we more or less all instantly perceive shifts in tension in a group of people, even when no one alludes to it. We can't control it, but we are connecting with others constantly whenever we are in their presence.
Outside of that, I don't know. The closest thing I've been able to compare to precognition is a powerful memory and knowledge of a person's behavior, which we can then use to accurately predict their future actions. As far as telepathy, some people have tons of experience and interest in social interaction, consciously see the general patterns and are usually the ones steering the direction of any social situation they're in. Others are tuned to see patterns elsewhere, and thus rely on their bodies to subconsciously communicate their true feelings to those better equipped to recognize them.