You could with a little work in June 2019, not sure what the picture is like now but it might be possible. I've used nix quite a bit on WSL2 which was surprisingly good.
If you can't do what you want in it, please open a ticket on https://github.com/Microsoft/WSL - there is also a repo for the kernel, but AFAIK technical feedback is best sent through this one.
(disclaimer: not directly involved with WSL, just trying to help)