No page number on \appendixpage

The page style of that appendix page is plain. You could temporarily redefine it to be empty:

\appendix
\begingroup
\makeatletter
\let\ps@plain\ps@empty
\appendixpage
\makeatother
\endgroup
\noappendicestocpagenum
\addappheadtotoc

The important line is just

\let\ps@plain\ps@empty

\makeatletter and \makeatother have been used to be able to work with @ in macro names, \begingroup and \endgroup limit the scope of this redefinition. So afterwards, plain is normal plain again.

Referring to lockstep's comment, you can do this in the preamble instead. Define

\makeatletter
\newcommand*{\myappendixpage}{%
  \begingroup
  \let\ps@plain\ps@empty
  \appendixpage
  \endgroup}
\makeatother

and later in the document just use it:

\appendix
\myappendixpage
\noappendicestocpagenum
\addappheadtotoc

Or redefine \appendixpage in the preamble:

\let\plainappendixpage\appendixpage
\makeatletter
\renewcommand{\appendixpage}{%
  \begingroup
  \let\ps@plain\ps@empty
  \plainappendixpage
  \endgroup}
\makeatother

Note, if you use \let in situations with a macro with optional argument or one made by \DeclareRobustCommand, use \LetLtxMacro of the letltxmacro package instead. Here, \let is sufficient.

Use the etoolbox package to patch the \@chap@pppage macro.

\documentclass{book}

\usepackage[titletoc]{appendix}

\usepackage{etoolbox}
\makeatletter
\patchcmd{\@chap@pppage}{\thispagestyle{plain}}{\thispagestyle{empty}}{}{}
\makeatother

\begin{document}

\tableofcontents

\appendix
\appendixpage
\noappendicestocpagenum
\addappheadtotoc

\chapter{Some title}

Some text.

\end{document}