It seems this will not work if the admin has disallowed Secondary Sign-in, which most school admins should have.
That setting is available here, and can be set to only the school's own Workspace domain, or blocking Secondary Sign-in completely.
If the goal is to block on all computers, then Allowing the school's domain is the right option, but if the need is to only block on Chromebooks and also block internal accounts, then using the Block alternative is right.
Trying this with an external account, I am blocked.
Trying this with an internal account, I am stuck on Verifying account after accepting the Terms Of Service.
One can, of course, also always URL block the mentioned address, chrome://chrome-signin as it shouldn't be needed for Chromebook users, and doesn't exist on other devices.