However I don't think the term Augments will be even brought up here. I think it's a reference less people would know about generally. Doesn't mean they won't use it but I don't believe they'll be taking pointers from 'Enterprise'.
"I told him that I could not only beam a grapefruit from one planet to the adjacent planet in the same system, which is easy by the way, I could do it with a lifeform. So, I tested it on Admiral Archer's prized beagle." -- Montgomery Scott, Star Trek
Besides, "Augments" is a handy word. It's distinctive, it's memorable, and it's more convenient than "eugenics supermen" or whatever terms were around previously. So who cares where it comes from? I use it because it works.