A few hundred milliseconds seems easily doable with a custom linux distro.

Unless your /dev/sda wants a fsck. :-)

is Ingenuity running Linux? All of the flight controller software i've seen for autonomous drones don't use an operating system.

Yep, from the article:

"This the first time we’ll be flying Linux on Mars. We’re actually running on a Linux operating system. The software framework that we’re using is one that we developed at JPL for cubesats and instruments, and we open-sourced[0] it a few years ago. So, you can get the software framework that’s flying on the Mars helicopter, and use it on your own project. It’s kind of an open-source victory, because we’re flying an open-source operating system and an open-source flight software framework and flying commercial parts that you can buy off the shelf if you wanted to do this yourself someday. This is a new thing for JPL because they tend to like what’s very safe and proven, but a lot of people are very excited about it, and we’re really looking forward to doing it."

[0]: https://github.com/nasa/fprime