Since quoted text is text, and a prenote is text, then quoted text can be the prenote (at the logical level).
At the practical level:
An experiment (using macros to store and enquote the text, for potential automation later):
\cite[\qmenquote{\qmuseq{q001}} \textemdash ][]{abook}
where \qmenquote is defined as
\newcommand\qmenquote[1]{\enquote{#1}}% from the csquotes package
and \qmuseq is defined as
\newcommand\qmuseq[1]{\csname qm:#1\endcsname}
with the CS qm:q001 being defined as
\expandafter\newcommand\csname qm:q001\endcsname{The cat sat on the mat.}
gives

for a given abook entry in the bib file and english option for csquotes.
A potential use for this could be where the prenote is a variable, and the \cite is "expanded" in one version to include the quote, and in the other version to have the cf (or a paraphrase, or nothing).
This suggests the possibility of being automatic in the "vertical" dimension, rather than (or in addition to) the "horizontal" direction - that is, for example, via a loop, or a conditional. An application could be as transliterations, versus translations, versus original text.
Last item in the list in the Code:
\RequirePackage{filecontents}
\begin{filecontents*}{\jobname.bib}
@book{abook,
author = {An Author},
title = {A Title)},
date = {2019-04-16},
location={A Location},
publisher={A Publisher},
}
\end{filecontents*}
\documentclass[12pt]{article}
\usepackage[english]{babel}
\usepackage[english=british]{csquotes}
%\usepackage[french]{babel}
%\usepackage{csquotes}
\usepackage[style=authoryear]{biblatex}
\addbibresource{\jobname.bib}
\expandafter\newcommand\csname qm:q001\endcsname{The cat sat on the mat.}
\newcommand\mycf{\textit{Vgl.}}
\newcommand\qmuseq[1]{\csname qm:#1\endcsname}
\newcommand\qmenquote[1]{\enquote{#1}}
\newcommand\qmaddsep[1]{#1\ \textemdash\ }
\newcommand\qmcite[3]{%
\if\relax\detokenize{#1}\relax \cite[\mycf][#3]{#2}\else
\qmaddsep{\qmenquote{\qmuseq{#1}}}\cite[#3]{#2}\fi}
\begin{document}
\begin{enumerate}
\item text: \qmuseq{q001}
\item enquoted: \qmenquote{\qmuseq{q001}}
\item with sep: \qmaddsep{\qmenquote{\qmuseq{q001}}}
\item quote with cite: \qmcite{q001}{abook}{S 123}
\item no quote with cite: \qmcite{}{abook}{S 123}
\item quote and no postnote: \qmcite{q001}{abook}{}
\item no quote and no postnote: \qmcite{}{abook}{}
\item \textbackslash textquote: \textquote[{\cite[S 456]{abook}}]{\qmuseq{q001}}
\item using the prenote \cite[\qmenquote{\qmuseq{q001}} \textemdash ][]{abook}
\end{enumerate}
\printbibliography
\end{document}
Besides \enquote, csquotes package also has the handy \textquote command.