Sure, possible. No real evidence for it though, in the sense that there is no identifiable communications link that would remove the isolated aspect of our isolated consciousness. The term "collective consciousness" (or even "the collective subconscious") is used to describe how group behavior seems to sometimes act as though isolated parts did communicate.
This is a philosophical discussion and thus there are many paths that we can follow if we assume that a linkage does exist, or we assume something about the nature of life and consciousness (awareness of self, perhaps?) that involves such a sharing or partitioning. This is somewhat along my pseudo-religious view of the nature of life and "soul", essence of life, being a subset of some universal "soul" that we are always part of and return into upon death. We are not individuals in the way that we get to be individual while inhabiting this biochemical machine, this shell or suit of armor, that we call ourselves.