However does a Heortling who undergoes this rite actually lose their Storm Rune (presumably replacing it with Death?)
/// I'd say no. People were born with the Conflict / Death Rune and it grew enough so that, on initiation day, they crossed the line drawn by Humakt's blade in the ground without hesitation and embraced Death. They didn't have Air to begin with. That, or they had it and died - and the Death Rune replaced their older Runes.
If the ritual is powerful enough to break the tie with the Storm rune in imitation of Humakt's own renunciation of the Storm rune, then maybe it is possible that a Chaotic convert to Humakt could lose his Chaos rune too. If not, then logically it should be a much longer process.
/// As a good heortling Humakti, I tell you no creature of the predark can initiate to the Sword. They'd be killed on sight before reaching the temple, and Humakt does not call to the predark anyway. This is all godlearner tripe and insanity. We know nothing about this death god the carmanian demons call by a similar name and do not want to know anything about it.
This isn't evidence that Humakt was illuminated, but it might be evidence that could help others to reach that conclusion (if they knew about Nysalorean Illumination and spirits of retribution, and few Gloranthans do)
/// Telling humaktis that their god is linked with gbaji and half-chaotic is a sure way of getting one's head cut off, making "evidence to help others" hard to get...