You definitely can. The experience is a mixed bag: they aren't often optimized for no-touch devices, and they often need more resources than low end devices can provide. But they definitely run without much work to install. I thought i was smart getting my kids Chromebooks but the frustrations about how poorly they run supercedes the value in my opinion.
Right, I'm sorry if I wasn't clear --- when I said "run in Chrome" I meant "in the Chrome browser regardless of OS, e.g. in Linux"
I want the kiddo to have not a Chromebook, but real Linux, e.g. Ubuntu. While the Android apps work fine, other things we do (e.g. easily saving files, dealing with local network stuff like Java Minecraft play) do not.
There is Waydroid. It doesn't use Chrome but should work on any Linux distro. I have used it in the past with some success, but not for quite some time now.