[platinum1]

The "control of the device" hasn't been handed over to anyone. If you log into another account, or go into guest mode, GoGuardian will not be present. In fact, you couldn't find out if GoGuardian was installed on another account you aren't logged into, because every account has all user data encrypted. The school won't be able to see anything about non cps.edu accounts - they don't know if they exist, what the email addresses were, etc.

There is no concept of installing or running programs outside of a login on ChromeOS. There is also only one form of device ownership, and that is device enrollment (which is not what is being described by OP), and the set of policies that are applied to enrolled device. Logging into an account cannot apply device policies.

cps.edu is who's enforcing that while you use a cps.edu account, you have to use their software (only while logged into that account or browser). BYOD devices are still yours and you can remove the account with a press of a button.