I'm 100% sure that CoT will allow us to make "born with it" / genetic factor mutation superhumans and roleplay as such with no problems. As to whether lore will help us justify and connect their existence into stories, I am highly confident there will be NPC mutants with backstories of their own, including mutants from birth, from which we can borrow references to some event that caused them to be born that way. Mutation is a hugely popular origin both in comics and was in CoH, so a successor game should contain some NPC mutants with backstories from each major mutant sub-origin as well.

We've also been told that there will be no "forced origin lore" wherein all mutants (or aliens or magic-users or ...) are assumed to have some common backstory elements. The devs (and we forumites) have generally agreed that a single lore-forced cause or beginning time (e.g. first atomic weapon test) for any superpower origin like mutants would be too restrictive on our ability to create characters. Our mutants could easily be said to come from any sub-origin imaginable, such as random gene mutation, science gone wrong, science gone right, self-caused by willpower, alien experiments, magic chimeras - whatever you want, and lore will never restrict it. The more unusual player creations will have to exist without solid lore roots or NPC examples, as you'd probably expect in any game.