I guess I just don't see it beyond a small scale. Maybe if Battletech cranked the Post/Transhumanism a lot, you might see MoC with a fad of "not having to be pregnant" or something, but it seems like what you're suggesting is cranking out hundreds if not thousands of random warrior creches.
Magistracy also has a memory of over 200 years where they had to survive on their own technology base, without Inner Sphere help, and while pirates were attacking them. So if the MoC ever went with Iron Wombs, they would make sure to have multiple backups of their technology records, multiple locations building them, and keep good records on non-IW pregnancy guides.
For me, Battletech having Post/Transhumanism would require a much more solid underlying technology base to be done properly.