Its hard to put too much behind that when the appendix says that whatever it was the Inchoroi physicians did, it killed all born children, all the women, and more importantly for this theory, nearly killed all the men.
Also, immortality as an unknown side-effect is unlikely, but the Inchoroi are prone to having many fall back plans. As you mentioned, the weapon races are a contingency plan, but so were Humans (the Tusk gift leading to the breaking-of-the-gates), and , likely, immortality.
For some unknown reason, the way the Inchoroi wanted to kill the Nonmen required them to treat them with something that would, if failed, make them immortal. So, their plan worked about 66% of the way (all women and children, many men), and they knew that immortality would slowly bring them to their cause. They had sranc to unleash from the north, and Huamns to attack from the south. They probably hoped that they would all be dead and not need the contingency plans, or that a dual attack from both sides would be sufficient to destroy the Nonmen, and even still, if all else failed, their mental faculties would slowly decline until they were no longer a threat and even fought for them. It would seem that the immortality gambit worked. Most, or at least many, of the surviving Nonmen fight with the Consult.
New(?) theory:
I think its more likely that the Inchoroi had no other way of doing what they did without the long-term effect of immortality. The Inchoroi are in decline at this point, the initial crash and war with the Nonmen sapped them of their strength and likely most of their knowledge of their own teknology.
What they ended up doing to the Nonmen might have been what the Inchoroi did to themselves, eons ago, with similar effects, killing all women and almost killing the men (or whatever their equivalent would be). It wasn't some new invention that they come up with, some new 'treatment' or use of the tekne, but an old, old technology that they could still extrapolate from and use as a weapon. The Inchoroi knew what would happened, planned to destroy the weakened nonmen that remained (Of Sranc and Men), and barring that, knew they had not the means to stay sane through the toll of ages, and would eventually go mad, either joining their side, or become easily disposed of.