Technically it will "work". But the window is not going to be decorated (no way to change focus, resize or move the window). Also, it will perform really badly on ARM Chromebooks because they do not have any 2D acceleration in X11 driver and the driver will have to update window over full screen Chrome window which will involve multiple CPU window copy operations.
And it will stop working at all when we will get rid of X11 entirely.
There are some online IDEs that allow developing on Chromebooks, which seem to be better suited for network/web oriented platform like Chrome OS.