I haven't tried running Eclipse. Oracle recently released an Early Access version of Java 8 with hardfp support to cash in on the Raspberry Pi fever, presumably that build would work on the ARM/Chromebook running Ubuntu (though it wouldn't be totally optimized for it) but I haven't tried it to be sure.
If I were doing Android development on this system I'd probably stick with ant based builds and use emacs or gedit (I wish Sublime Text 2 had an ARM build, the fact that it doesn't is kind of killing it as a useful editor for me these days). Eclipse is already a bit slower than I would like on my desktop, I'd imagine using it wouldn't be that great on the Chromebook.
But I don't think the Android SDK is available in anything but x86... so, maybe if he used qemu emulation?
[0] https://chrome.google.com/webstore/detail/secure-shell/pnhec...
Is it possible to install Java+Eclipse+Android SDK on it?