Short answer: no.
Long answer:
The only ways an automated script can know that the output should contain the word "Proof" are:
1) This knowledge is hardcoded in the script. It knows about the meaning of some latex commands and environments (the via taken by pandoc)
2) It can run tex code and get the output (via taken by t4ht, for example)
The first approach is not flexible enough, since you can load packages which are not known by the script, and which define commands that will be ignored (in addition, your document can define your own commands too).
The second approach can be done via pdflatex
followed by some "pdf to text" converter, or via latex
followed by dvi2tty
, or via tex4ht
. In any case, it loses the original tex markup, and then is not appropiate if you want to keep the "code" of the math formulae.
Let's see an example. Consider the following document:
\documentclass{article}
\usepackage{nopageno} % No page numbers
\usepackage{amsthm}
\begin{document}
\begin{proof}
This is a proof
\[
\sum_{i=0}^\infty x^2
\]
\end{proof}
\end{document}
Running it through standard pdflatex
you get:

If you run it through pandoc
, you get the following .txt
:
This is a proof $$\sum_{i=0}^\infty x^2$$
in which you lost the word "Proof", and the final end-of-proof mark, but it keeps the formula markup.
If you run it through pdflatex
and then pdftotxt
you get:
Proof. This is a proof
∞
x2
i=0
which keeps the word "Proof", but completly messes the formula
If you run it through latex
and then dvi2tty
, you get:
Proof. This is a proof
1X
x2
i=0
|___|
Which is closer to the pdf output, but still loses the formula markup.
If you run it through tex4ht
you get an HTML version of the document, which can be in turn processed by pandoc
to get the following .txt
:
Proof. This is a proof ∞ ∑ i=0 x2 \_\_
As you can see, none of the solutions is satisfactory.