So this seems to work:
\documentclass{minimal}
\usepackage{fontspec}
\usepackage{unicode-math}
\setmathfont{XITS Math}
\usepackage{siunitx}
\sisetup{%
detect-all,
}
\newcounter{works}
\setcounter{works}{0}
\usepackage{pgffor}
\begin{document}
\newcommand{\ifavailablethenelse}[4]{%#1=font,#2=charcode,#3=then-clause,#4=else-clause
\setcounter{works}{0}
\bgroup
\font\test="#1" \test
\ifnum\XeTeXfonttype\font>0
\ifnum\XeTeXcharglyph"#2>0
\setcounter{works}{1}
\fi
\fi
\egroup
\ifnum\theworks=1
#3
\else
#4
\fi
}
\sisetup{math-celsius=foo}
\foreach \phont in {Asana Math,XITS Math, STIXGeneral, Neo Euler}
{
\ifavailablethenelse{\phont}{2103}{\sisetup{math-celsius=℃}}{%
\ifavailablethenelse{\phont}{00B0}{\sisetup{math-celsius=°C}}{
\sisetup{math-celsius=nix}
}
}
\setmathfont{\phont}
\(\SI{123}{\celsius}\)
}
\sisetup{text-celsius=bar}
\foreach \phont in {DejaVu Serif, Linux Libertine O, TeX Gyre Pagella,
Arial}
{
\ifavailablethenelse{\phont}{2103}{\sisetup{text-celsius=℃}}{%
\ifavailablethenelse{\phont}{00B0}{\sisetup{text-celsius=°C}}{
\sisetup{text-celsius=niente}
}
}
\setmainfont{\phont}
\SI{123}{\celsius}
}
\end{document}
Albeit, it seems to be slow.
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