Yup it would trigger a restart -- that first link details some other options if restarting the workload is absolutely not an option. You can debug a copy, start a privileged pod, or jump on to the node and actually enter the namespace manually. At the end of the day all these containers are just sandboxed+namespaced processes running on a machine somewhere, so if you can get on that machine with the appropriate permissions then you can get to the process and debug it.

Of course, if you're in a tightly managed environment and can't get on the nodes themselves things get harder, but probably not completely impossible :)