If I understood your question correctly, to add the word "Appendix" in the ToC, you can redefine \cftappendixname; if you also want to suppress the numbering for the appendix (both in the ToC and in the body of the document), you can redefine \thechapter just before the appendix (and adjust \cftchapternumwidth). Here's a little example:
\documentclass{memoir}
\usepackage[dutch]{babel}
\addto\captionsdutch{%
\renewcommand{\appendixname}%
{Appendix}%
}
\renewcommand*\cftappendixname{\appendixname}
\begin{document}
\tableofcontents*
\chapter{Test Regular Chapter}
\appendix
\addtocontents{toc}{\setlength\cftchapternumwidth{1em}}
\renewcommand\thechapter{}
\chapter{Test Appendix}
\end{document}
