What sort of immortal are we talking about? And is anything else changing?
Generally, yes, depending also on what you mean exactly by “religion”.
I think spirituality, cosmology, myth and metaphor are the core and useful aspects of religion, for which there is a need and a human nature to create, even in the absence of a formal agreed religion.
If by religion you mean the crusty crappy version we see a lot of, with little or no real spirituality and a whole lot of dogma, hierarchy, tithing, rules, xenophobia and control-freakiness, then hopefully not.