Convert numbers in string to string

You can do it expandably, provided the string only has alphanumeric ASCII characters:

\documentclass{article}

\makeatletter
\newcommand{\convertdigits}[1]{\expandafter\convert@digits#1\convert@digits}
\def\convert@digits#1{%
  \ifx#1\convert@digits
    \expandafter\@gobble
  \else
    \expandafter\@firstofone
  \fi
  {\convert@@digits#1}%
}
\def\convert@@digits#1{%
  \ifnum9=9#1%
    \expandafter\@gobble
  \else
    \expandafter\@firstofone
  \fi
  {\convert@@digit#1}\convert@digits
}
\def\convert@@digit#1{%
  \ifcase#1%
    zero\or
    one\or
    two\or
    three\or
    four\or
    five\or
    six\or
    seven\or
    eight\or
    nine\fi
}
\makeatother

\begin{document}

\def\myvar{A12Z4E}

\convertdigits{A12Z4E}

\convertdigits{\myvar}

\edef\myvartext{\convertdigits{\myvar}}
\texttt{\meaning\myvartext}

\end{document}

A different expl3 implementation: the argument to \convertdigits is fully expanded before being examined and scanned item by item.

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn

\NewExpandableDocumentCommand{\convertdigits}{m}
 {
  \guuk_convertdigits:e { #1 }
 }

\cs_new:Nn \guuk_convertdigits:n
 {
  \tl_map_function:nN { #1 } \guuk_digit:n
 }
\cs_generate_variant:Nn \guuk_convertdigits:n { e }

\cs_new:Nn \guuk_digit:n
 {
  \str_case:nnF { #1 }
   {
    {0}{zero}
    {1}{one}
    {2}{two}
    {3}{three}
    {4}{four}
    {5}{five}
    {6}{six}
    {7}{seven}
    {8}{eight}
    {9}{nine}
   }
   {#1}% not a digit
 }
\ExplSyntaxOff

\begin{document}

\def\myvar{A12Z4E}

\convertdigits{A12Z4E}

\convertdigits{\myvar}

\edef\myvartext{\convertdigits{\myvar}}
\texttt{\meaning\myvartext}

\end{document}