It depends on your definition

Whether there is a god or not depends upon your definition of god. (See my blogs of 10 June and 3 July 2017.) Similarly, the question of digital immortality depends upon your definition of immortality. My argument against the possibility of human immortality can also be leveled against AIs (see my blog of  15 Oct 2010). But one might also consider the possibility of an immortal society * of (specialist?) AIs. And if one believes in the block universe interpretation of relativity theory I suppose we are all immortal in some sense even as things stand today. This all points once again to the importance of scientific pluralism.

* perhaps a society that has even formed a concept of its self