Actually no, it's a trope that most often occurs in books with an agnostic or atheistic background, and what drives the thanatophobe to search for immortality at any cost is usually not the fear of damnation but the fear of nothing - the fear that his (it's usually a he) supremely valuable ego will cease to exist. It's a subject worthy of study by any literature student in search of a thesis topic.
The only exception I know of is Huxley's "After Many A Summer," which is a literary exploration of the ways people handle the fear of death. The major thanatophobe there is driven by a simplistic fear of hellfire (to the point where he considers an immortality treatment even after learning that the price is to regress to an animal existence), but the author himself clearly pities the character for being a prey to such superstition: if Huxley believed in the survival of the soul, he inclined to a concept of merging with the All, not individual judgement.