Just curious, seeing as how it's a "creative" OS, I don't know how functional it could be on Chromebook.
Can I install Ubuntu Studio on a Chromebook?
Can you install Ubuntu Studio on your particular model of Chromebook, I couldn't possibly know.
Will all the included applications perform up to your needs? I couldn't possible know.
Ubuntu Studio is just Ubuntu with select pre-installed applications. I have a similarly built OS based on Ubuntu running on my CR-48 Chromebook.
There are 2 main ways of running a full Linux OS on Chromebook, Crouton which does not remove ChromeOS, and a full install.
If you want to go all the way with a full install and remove ChromeOS, you need to install a new BIOS before booting your install media and installing as normal.
I would actually recommend using something like GalliumOS which is based on Ubuntu and designed for use on Chromebooks. You could then install the same apps as Ubuntu Studio has.
Even if using a standard Ubuntu Studio install image, much of the documentation from GalliumOS wiki will apply, like this install page.