is it actually POSSIBLE to install Linux and not with some sub-system?
 

I'm on a ASUS C204 Chromebook (controlled by my school) is it possible to run a Live version of Linux or even get Linux on a HDD?

Addressing just the technical aspects of the question it looks like a "bare metal" approach is not possible on that model, at least not until some firmware changes become available. Scroll down to Asus C204 : https://mrchromebox.tech/#devices

Otherwise, you might look at Crouton.

Perhaps a political approach might be to ask the IT dept, if there is one and not just a bunch of M$ resellers, about which method of running GNU/Linux natively would be recommended.

What goals to you hope to achieve after getting GNU/Linux running? Maybe a single-board computer could be an option.

I find a "flip" C204, is that normal?

No idea, but that is the only C204 in the list. There are no check boxes in the RW_LEGACY Firmware and UEFI Firmware (Full ROM) columns. So it is not supported yet.

Crouton might still be an option, depending on how helpful the school staff are.

Bolded a part above for emphasis only. Aside from any technical issues, you need to exercise some caution here. If it's the schools device, given to you for school use, it comes with strings attached. Doing something outside the scope of what's allowed can have repercussions...what they are is up to the school.

Before continuing with anything, I would suggest talking to someone at the school, and explaining why you want to do this, as asking if it's ok. The outcome will be one of the following:

• You're allowed to (and get that in writing)
• You're NOT allowed to, because it's their device and they have to have it a certain way to manage things
• They give you a second device to do this on

Yes, extremely important point! Written approval goes without saying and thus went unsaid, until now. Getting permission in writing for this kind of activity is very important. Having it in writing is almost more important than the permissions themselves. Also keeping paper copy around can be a good form of insurance. School staff can be great about these kinds of things and encourage learning or they can demonstrate the worst sort of microsoftianism and smallness. The key is to find out in advance which your school staff are, and get approval documented in writing in advance. It is cheaper and easier than having to lawyer up at a later date, especially if they try to go back on what they said.

Even if they say no, you might be able to buy an inexpensive used laptop at a repair shop. Then you'd have a free hand to try any distros that you want to.

You can run various version of Linux on Chrome without Crouton if it is supported, which most new devices are.
It will use LXD and allow you to change the Linux OS and have multiple containers: https://discuss.linuxcontainers.org/...hromebook/3823

Since this is a managed system, it is probably locked so you can't enter developer mode which is needed to install Linux natively and not in a container.
If you can get developer mode enabled, then you can follow the steps at https://chrx.org/ and the script there to dual boot or take over the whole drive. Assuming your hardware is supported.

This is the answer, as far as I'm concerned. I used to be IT in a K12 school. With limited resources, and concern for security, the likelihood they'll either let you modify their equipment, or provide you extra equipment, is pretty low. That is, unless you can give them a really good reason, such as project requirements, or availability of software that isn't available on their current ecosystem.