Not quite yet, but we're working on it. There are some significant features that KaTeX doesn't yet support, but we're working to add them in the near future.
In the meantime, you could use our TeX React component to use KaTeX when possible, and fall back to MathJax only when necessary: http://khan.github.io/react-components/#tex
Sorry to tl;dr your code, but how exactly is it based on TeX? Do you actually run Knuth's TeX code to make this work, or did you reimplement it?
Also, kind of irrelevant, do you think we'll ever get something better than (La)TeX syntax? I've been frustrated by obscure error messages from LaTeX in big documents because it's a macro language, so the interpreter doesn't actually see what you're typing. How does KaTeX handle errors?
Also, we attempt to have relatively good error handling! If you open up the javascript console on the main page and type in a bad expression, you can see what the errors we throw look like. We're not planning on supporting anything other than LaTeX syntax for now though, unfortunately.
We're using the similar fonts to what MathJax uses (ours have some slight changes in spacing), but we do our own layout calculations to be much faster.
Most inline math is done, but we're missing a bunch of individual symbols (see CONTRIBUTING.md in the repo if you'd like to contribute!) The main things we're missing are environments (i.e. \begin and \end), but we'll be working on those soon!