If you want the Chromebook to remain a 'Google Chromebook' than the answer is no, unfortunately. You're at the mercy of what you can utilize in the Chrome web app. store..however, Chromebooks with developer mode enabled make, in my opinion, the perfect little cheap machine to run your favorite distro of linux (Kubuntu for me). And it's literally a few key presses in the terminal and voila, you've got a linux box capable of running everything and anything. You don't even have to choose Chromebook or Linux either, you can very easily have them installed and capable of running concurrently, in a matter of a few keystrokes.I'm not quite sure what 'everything and anything' means. Do you install Linux and then set up a virtual environment to run Windows in, so you can run iTunes? Is there even enough memory in a Chromebook to support such an abomination? And can you get back to Chrome afterwards? It sounds like a frigging nightmare.
Probably should just wait a bit until someone develops an iPod loader for Chromebooks.
*This isn't quite true. CNET has a Windows program that claims it will load your iPod. Doesn't help me, but at least we aren't locked into Apple.