No, this is not a good account of descriptivism vs prescriptivism.
All of the true rules of language are empirical rules that everyone agrees upon. We all know that “Henry cheese eats” is not grammatical in any dialect of English (although it is in Japanese). There are many other such rules that we all tacitly (and usually unconsciously) agree on: if you take a dozen words, only a tiny fraction of the millions of possible arrangements of those words are grammatical, and all native speakers know instantly which are valid in their language.
Descriptivist linguistics (among other things) studies empirical language and works out what abstract unconscious consensus rules native speakers are following.
We take for granted the vast majority of rules in our language - we absorb them unconsciously when we learn language as young children, and every native speaker of a given dialect follows and agrees on the same rules without conscious effort. Most of us can’t consciously articulate what those rules are, yet we use them flawlessly to build sentences. And nothing in this vast majority of real rules requires prescriptivists to coach us.
So how do prescriptivists fit into this picture? Prescriptivists ignore the vast majorty of rules that I have described above - of course, because we all agree on them and follow them effortlessly and flawlessly. Instead, the prescriptivists obsess over is a tiny fraction of insignificant semi-rules. These are either situations on which there is no clear empirical consensus - perhaps something in flux in the language, or variation between close dialects or registers; or they are completely invented notions, not rules that native speakers ever follow at all in practice. And prescriptivists generally express a concern that if we don’t all follow their precise recommendations on the tiny proportion of “rules” that they obsess about then nobody will be able to communicate clearly and civilization will rapidly disintegrate.