TeX has \def which basically allows you to write lambda expressions, so yeah it's Turing complete. The basic math notation isn't though, and I'd be surprised if this extension allows you to use \def (or really any of the more powerful features of TeX).

If it's using the full selection of functions available to KaTeX, here's the list:

https://github.com/Khan/KaTeX/wiki/Function-Support-in-KaTeX

\def isn't included in the core set, from what I can see.

Being turing-complete doesn't prevent you from emulating it. Also the subset of math expressions should be pretty simple.