I don't think the DNS exercise would behave the same although that probably depends on how the container was setup. Docker usually controls /etc/resolv.conf. Another exercise is "try to figure out if you're in a container or VM so that'd definitely be different"
The question is not if the exercises would behave identically, but if you can test the objective in a container. For example, you can totally test, screw up, and fix DNS in a container. I would think that "try to figure out if you're in a container or VM" would be exactly the same as it is right now.
* Boot problems, such as: GRUB config/install errors, kernel parameters, init startup errors, blocking processes
* Many network scenarios, such as: PXE issues, multipath, load-balacing, anything requiring configuring network interface settings, firewall configuration.
* Resetting an unknown root password
* Booting directly to bash
* Filesystem mounts through fstab or systemd mounts
There's probably more I could think of, but I think that's a good list.