This works, but the length you get is quite unpredictable, because it depends on the current text direction.
\documentclass{article}
\usepackage{tikz}
\usepackage{luatexja}
\begin{document}
\tikz{\coordinate[yshift=\the\expandafter\ht\expanded{\strutbox}];}
\end{document}
It also works when \strutbox is just a box register name, because it's unexpandable and so \expanded returns \strutbox.
In order to make this work with ProfCollege, you can patch the macros in the package that use the construction
\documentclass{article}
\usepackage{ProfCollege}
\usepackage{luatexja}
\usepackage{etoolbox}
% the abstract version of the above
\newcommand{\getstrut}[1]{%
\the\expandafter#1\expanded{\strutbox}%
}
% the internal commands of ProfCollege to patch
\patchcmd{\TikzPH}{\the\dp\strutbox}{\getstrut\dp}{}{}
\patchcmd{\TikzPHD}{\the\dp\strutbox}{\getstrut\dp}{}{}
\patchcmd{\TikzPHD}{\the\dp\strutbox}{\getstrut\dp}{}{}
\patchcmd{\TikzPB}{\the\ht\strutbox}{\getstrut\ht}{}{}
\patchcmd{\TikzPBD}{\the\ht\strutbox}{\getstrut\ht}{}{}
\patchcmd{\TikzPBD}{\the\ht\strutbox}{\getstrut\ht}{}{}
\patchcmd{\TikzRH}{\the\ht\strutbox}{\getstrut\ht}{}{}
\patchcmd{\TikzRB}{\the\dp\strutbox}{\getstrut\dp}{}{}
% the user level command to patch
\patchcmd{\FlecheLineaireH}{\ht\strutbox}{\getstrut\ht}{}{}
\begin{document}
\Pourcentage[Calculer]{15}{39}
\verb+\hanzibox*[frametype=none]{我}[wo3][moi]\\[1ex]+
\begin{center}
\Propor[
Stretch=1.25,
Math,
GrandeurA=Hauteur $h$ (cm),
GrandeurB=\begin{tabular}{c}Volume (en cm$^3$) d'un cylindre\\ de rayon \Lg{5} et
de hauteur $h$\end{tabular},
Largeur=0.75cm
]{2/$50\pi$,3/$75\pi$,5/}
\end{center}
\FlecheLineaireH{1}{2}{3}{$+$}
\FlecheLineaireB{1}{2}{3}{$+$}
\end{document}
The only user level command that uses \ht\strutbox is \FlecheLineaireH, quite strangely without \the, but I copied the example from the package documentation and it seems to work.
The previous caveat still applies: if you use different text directions as allowed by luatexja, you'll get into troubles.

\strutbox:) Since\tikz{\coordinate[yshift=\the\ht\strutbox];}is part of a command of the packageProfCollegeI'm using, I can't change it. I'm facing the same problem as in tex.stackexchange.com/q/643376/18401: my real document makes use ofluatex-jafeatures only exceptionally. So, is there a way to load them only locally in order they don't interfere with other parts of the document?lualatex, which has to display in a (single) listing (typeset in monospaced font) both Latin and Chinese characters. I load it with\usepackage{luatexja-fontspec} \ltjsetparameter{jacharrange={-9}} \setmainjfont{FandolSong}.