Not if it's a hardware key. You give the processor something you want to encrypt, but you can't look at the actual key itself (the only way to do that would be with an electron microscope).

That said, if you could gain persistent remote access to the computer, you can just repeatedly ask the processor to encrypt things.

This is incidentally part of why the Chromebook design makes it hard to persistently change the machine; a reboot starts from a clean signed image and then mounts a home directory. It's still possible to stick a persistent exploit somewhere in the home directory, but it's not as simple as just dropping a file in /etc/init.