Can I use nicefrac within siunitx?

For cases where you want to do things beyond the understanding of the siunitx internals, you can turn the parser off

\SI[parse-numbers = false]{2\nicefrac{1}{2}}{\minute}

The option fraction-function=\nicefrac option will do just that, but you'll need to load the package nicefrac and set quotient-mode = fraction as well.

\documentclass{standalone}

\usepackage{nicefrac}
\usepackage{siunitx}

\sisetup{
    quotient-mode = fraction,
    fraction-function=\nicefrac
}

\begin{document}
    \nicefrac{1}{3} \num{1/3}
\end{document}