You have to define a symbol font and assign a math code to the Armenian letters.
Here's how one could do it; it's important that the code is just after the \newfontfamily
command. You can use another font, provided it has the required glyphs. Probably the best approach is to use a different name altogether, maybe pointing to the same font:
\documentclass[a4paper]{article}
\usepackage{polyglossia}
\newfontfamily{\armenianfont}{DejaVu Serif}
\newfontfamily{\armenianmathfont}{DejaVu Serif}
\ExplSyntaxOn
\DeclareSymbolFont{armenianletters}{\g_fontspec_encoding_tl}{\l_fontspec_family_tl}{m}{it}
\int_step_inline:nnnn { "531 } { 1 } { "556 }
{
\Umathcode #1 = "0 \symarmenianletters #1 % low level call
}
\int_step_inline:nnnn { "561 } { 1 } { "587 }
{
\Umathcode #1 = "0 \symarmenianletters #1
}
\ExplSyntaxOff
\setmainlanguage{armenian}
\begin{document}
Text: հայերեն english
Math: $հայերեն english հայերեն^2$
\end{document}