Hi!
I was a Chromebook (ARM) owner and the "run Linux and ChromeOS together" is just run another DE in a chroot environment BUT both DEs are using the same kernel and structure.
Maybe (MAYBE) you could run Core on it, but as Core is not a "usual" distro and does stuff in a (good) different way, maybe you will end up loosing the ChromeOS DE and default (not web) apps.