Broadly no, largely because neon's been around for more than 100 years. It might have retained 'state-of-the-art' newness as a metaphor for 'modern' until not-long before the Moon landings but like The Sound of Silence, those are today “so last century." (Though they seem like yesterday to people like me. Ouch!)
If it ever was common to use "neon" as a metaphor for "modern" that wasn't "in daily life" and it's no longer a thing.
That is indeed a way of agreeing "neon" is too old-fashioned since it's an old technology.
One counterpart of "neon" in use nowadays might be "silicon" which could already be passé but certainly isn't alone. Others include "wet-ware" meaning brain matter as opposed to hard- or soft-ware…
There are also inverted references such as "snail-mail" comparing slow traditional paper post to nearly-instant e-mail.
I doubt "neon" is still used to make literature or other arts "fancier"… if it ever was. Did The Sound of Silence try to make itself "fancier" or did it legitimately use a colourful (no pun intended), graphic term for dynamic effect? The point being that "fancier" is more about a bogus method than a better result.
Is it fair to cite '新世紀' or '新世紀エヴァンゲリオン' without English phonetic spelling and full literal translations? Still, "neon genesis" is much too far from "new era" to be anything but an artificial construct, forced upon the words for the convenience of the author.
"If I used it in a small talk, can a random listener understand what I mean" throws up more and different topics.
Quite separately, "random listeners" are people met in lifts or queues with whom we have nothing apparent in common. What we say to them is at best "chit chat", which has even less value than ”small talk."
By contrast "small talk" is with people we have at least some reason to want to be with, as on dates or at parties…
Further ”a small talk" always means "a short lecture”; never social intercourse.
Beneath any of that, the parts of any sentence must match in number, tense and every other way: you need either "If I use it… can a listener… ?" or "If I used it… could a listener… ?"