On my chromebook I use crouton[1], which is arguably more "native". You get an Ubuntu install in a chroot and can even run X11 apps in a chrome window. I was even able to compile neovim, you just need to set it up to use the system's lua and luarocks.
They would likely restrict play store installs, and currently there is no way to side-load Android apps; the normal Android developer mode options does not allow side-loading anyway, much less an enterprise managed device. I don't think there's any way to "restrict" dev mode, necessarily... anyone can put any Chromebook into dev mode, and lose all data that was on it in the process.
You might also look at Servers Ultimate Pro from Ice Cold Apps. It has.... many servers. Perhaps too many. Perhaps enough that it looks like a "Hold my beer" response to a question about how many servers could actually be compiled for Android.
I wouldn't run most (any?) of them on a connection exposed to the real world, but at least in theory if you want to run an AAMP stack I believe you could, though on a quick glance you might actually have to be content with Nginx. You can also provide your own little bit of Gopherspace if you so desire.
I'm still waiting for Amazon to restock after I saw this post go up: https://blog.lessonslearned.org/building-a-more-secure-devel...