Corey Cook answers
In short, my answer is "no." This is simply because all that makes us "human" is in light of our mortality. As social animals, the psychological traits, cognitive capacities, and social structures we have developed are all directly related to the challenges of survival within interdependent groups. If we were unconcerned with survival, we would not be subject to the biological laws of evolution and would not resemble any living being that we currently have any knowledge of. In other words, we couldn't possibly be human.
My more imaginative answer has to do with the nature of the "immortality." If a human were to somehow become immortal, or even magically give birth to immortal offspring, they would still possess the genetic blueprint of human cognition, and would therefore still be concerned about mortality, social structures, and other existential concerns. If an immortal creature existed that never would have had to develop such capacities, they likely never would have needed to develop any form of religious belief system to account for such existential concerns, and likely wouldn't care or have a need for atheism, religion, prejudice, or any other uniquely human phenomenon.
Corey Cook is a lecturer in the School of Interdisciplinary Arts and Sciences at the University of Washington Tacoma.