Excellent question! In this regard, I assume that the style of immortality being discussed is regenerative, such as Deadpool or Wolverine? In these instances, immortality would still be applicable to an extent. Situations that would cause instantaneous death (being burned alive, decapitation, crushed) would still stick.

In other situations, a location may have power dampening effects in play that would make death more likely; in scenarios like this, we'd be sure to forewarn you.