Sure, just define the environment in this way in the document:

%%%%%%%%%%%%%%%%%%
\documentclass{article}
\NewDocumentEnvironment{foo}{+b}{}{}
\NewDocumentEnvironment{latexenv}{}{}{}
\long\def\FooCmd #1\EndFooCmd{}

\begin{document}

normal text

\begin{foo}
<p dir="auto">The following code shows the concept:</p>

<p dir="auto">This is another paragraph</p>
\end{foo}

normal text

\begin{latexenv}
$$E = mc^2$$ And this is \textit{latex}.
\end{latexenv}

\FooCmd
<p dir="auto">The following code shows the concept:</p>

<p dir="auto">This is another paragraph</p>
\EndFooCmd
\end{document}
%%%%%%%%%%%%%%%%%%%

And then redefine it to eat the argument in the configuration file:

%%%%%%%%%%%%%%%%
\Preamble{xhtml}
\ScriptEnv{foo}
{\ifvmode\IgnorePar\fi\EndP\NoFonts\hfill\break }
{\EndNoFonts }

\ScriptCommand{\FooCmd}
{\ifvmode\IgnorePar\fi\EndP\NoFonts\hfill\break }
{\EndNoFonts }
\RenewDocumentEnvironment{latexenv}{+b}{}{}
\begin{document}
\EndPreamble
%%%%%%%%%%%%%%%%

Ideally, you can define the \FooCmd and \EndFooCmd in the preamble, or in a custom package, and then redefine it in TeX4ht configuration file:

%%%%%%%%%%%%%%%%%%%%%%%
\documentclass{article}
\NewDocumentEnvironment{foo}{+b}{}{}
\long\def\FooCmd #1\EndFooCmd{}

\begin{document}

normal text

\begin{foo}
<p dir="auto">The following code shows the concept:</p>

<p dir="auto">This is another paragraph</p>
\end{foo}

normal text

\FooCmd
<p dir="auto">The following code shows the concept:</p>

<p dir="auto">This is another paragraph</p>
\EndFooCmd
\end{document}
%%%%%%%%%%%%%%%%%%

The configuration file could contain the TeX4ht commands from my previous post:

%%%%%%%%%%%%%%%%%%%%
\Preamble{xhtml}
\ScriptEnv{foo}
{\ifvmode\IgnorePar\fi\EndP\NoFonts\hfill\break }
{\EndNoFonts }

\ScriptCommand{\FooCmd}
{\ifvmode\IgnorePar\fi\EndP\NoFonts\hfill\break }
{\EndNoFonts }
\begin{document}
\EndPreamble
%%%%%%%%%%%%%%%%%

way cool, thanks Michal.

Michal, or anyone, is there an alternative to \HCode that outputs its argument completely verbatim, ideally including line breaks?
It seems \HCode outputs a surrounding <p> and </p>.

It seems \HCode is inscrutably defined in the scripts, such as htlatex. At first glance, the definition makes no sense to me at all :).

Thanks.