They would get roflstomped by LNS caps, because whatever happens IRP never reflects what goes on ingame.
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It's explicitly stated in the Vanilla campaign that humanity is too strong for the Nomads and thus they needed their infection scheme. Unless they pull a major "that was only an expedition, here comes the real army" stuff, the nomads couldn't defeat a more or less united humanity.
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Vanilla lore (yes, that stuff people always forget about,) does state that Nomads are highly adaptive. Logically, their combat prowess has increased substantially over time as infiltration failed. Because changing their tactics is what they do.
Regardless, they don't have the military strength to overwhelm humanity, will lose and will attract much more attention than they want to. And, again, killing humanity is but a "sidequest" for them.