You should use
\begin{equation}
S_\textup{ном.} = S_{123}
\end{equation}
because that's text.
You can consider using unicode-math instead of mathtext
\usepackage{amsmath}
\usepackage{unicode-math}
\setmainfont{Times New Roman}
\setmathfont{XITS Math}
% \newfontfamily\cyrillicfont{Times New Roman}
\usepackage{polyglossia}
\setdefaultlanguage{russian}
but notice that amsmath must be loaded before it. This wouldn't change the way you input that subscript.
XeTeX introduced new primitives such as \Umathcode (up to version 0.9998 called \XeTeXmathcode, renamed for compatibility with LuaTeX) that's the Unicode analog of \mathcode.
What does \mathcode in traditional TeX? A declaration such as
\mathcode`+="202B
tells TeX that a + in math mode should be treated as a binary operation symbol (leftmost byte "2), taken from font family "0 and slot "2B in the corresponding font. In the same vein, one can say something like
\Umathcode`∑="1 "1 "2211
or even
\Umathcode`∑="1 "1 `∑
The primitive \Umathcode has the syntax
\Umathcode<Unicode point> = <math type> <family> <slot>
After the (optional) =, three numbers should be given, because packing the information into a single number as done by TeX is not possible. Actually the information is still packed into a single number (in this case it's decimal 18883089, hexadecimal "1202211), but the translation from packed number to explicit type-family-slot is not straightforward.
This will be probably accompanied by a similar declaration
\Umathchardef\sum="1 "1 "2211
so that typing $∑$ or $\sum$ will give the same result.
The unicode-math package loads a huge list of symbols and performs assignments similar to the one for ∑. The number corresponding to ∑ will be different, because it depends on many aspects which can't be covered in a short answer.
Actually unicode-math does much more than this, because it sets things up so that commands such as \mathbf or \mathrm give the desired result.
There are other primitives corresponding to the traditional ones, namely \Umathchar, for using a directly specified character, or \Udelimiter for setting delimiters with normal and large variant, \Umathaccent and finally \Uradical for defining root symbols. See texdoc xetex that will open “The XeTeX reference guide” by Will Robertson and Khaled Hosny.
Best Answer
I don't know anything of Devanagari and Sanskrit; but here's an example that I obtained first by compiling without the second line, then copying from the PDF and pasting.
As far as I can see, the two lines are identical.
The lines
have the same effect as your
but use XeTeX more efficiently.