Il est possible de redéfinir la commande `\makebackcover` afin d'y insérer une image
\documentclass[mainlanguage=english]{yathesis}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{mwe}
%
\pres[logo=example-image]{My COMUE}
\institute[logo=example-image-a]{My Institute}
\company[logo=example-image-b]{My Company}
\laboratory[logo=example-image-b]{My Laboratory}{Address of my laboratory}
%
\makeatletter
\def\makebackcover{%
\YAD@alarm@noabstract%
\cleardoublepage%
\pagestyle{backcover}%
\YAD@abstract@page\par%
\centering\includegraphics{image-c}
}%
\makeatother
\begin{document}
\title[Fou]{Foo}
\author[chupin@ljll.math.upmc.fr]{Maxime}{Chupin}
\maketitle
%
\makelaboratory
%
\begin{abstract}
\blindtext
\end{abstract}
\begin{abstract}
\blindtext
\end{abstract}
%
\makeabstract
\mainmatter
\chapter{Foo}
\blindtext
\backmatter
\makebackcover
\end{document}
