No.
> Namely, that it doesn’t exist.
That it isn’t a representation, it is a fact about the universe (not the resource, because existence is not a predicate) which is inconsistent with their being a representation. A resource must exist to have a representation.
Since a resource that does not exist cannot have any representation, it is therefore impossible for a representation to be found of such a resource. In fact, other than in the case where 421 is the correct response (“don’t ask me, I’m not responsible for that URL”) or where 406 is a more specific response than 404 (“I have the resource requested, but can’t produce a representation in the format you have requested, and don’t want to waste both of our time sending you a format you may not be able to use”), the only reason for a 404 is that the resource does not exist.
>The 404 (Not Found) status code indicates that the origin server did not find a current representation for the target resource or is not willing to disclose that one exists.
So when you say:
>yet the record doesn't exist, then the resource doesn't exist.
So you do have a current representation for the target resource. Namely, that it doesn't exist.