No, immortals cannot have children.
Based on the provided reference, immortality isn't a hereditary trait; it's a random occurrence. As Connor MacLeod states in Highlander: Endgame, immortals have existed "in the days before memory," implying their presence is ancient and not tied to lineage. The reference states specifically that "They cannot have children, so it is not a gift that is passed down." This clearly indicates that immortality is not a genetic trait passed from parent to child.
In summary, the ability to be immortal is not something that can be inherited or passed down to offspring.
