Emergent is in all the major dictionaries, in the OED’s case since 1891, albeit relating to an emergency is only one meaning (earliest cite in the OED is 1706). The meaning I’m more familiar with is arising spontaneously, as in “consciousness is an emergent property of a complex neural network.” But I’ve read a lot of literature about evolution, which may be why I’m more familiar with that sense.
Google Ngrams has hits for nonemergent going back to the 1880s, but the term really takes off in the 1970s, as Kurwamac notes.
Dictionaries don’t create separate entries for every non- and un- addition to a root, but it seems to me that this is one for which they should. If, as I suspect, nonemergent is mainly confined to the medical field the editors simply may not have noticed it yet. The OED entry for emergent, in particular, is particularly decrepit.