What happens when the kernel_task is killed? What happens when you kill kernel_task on OS X? Is that even possible? I know that the system reboots because of kernel panic when you kill launchd, but I can't find any resources online and am afraid of trying to kill kernel_task.
You can't properly kill kernel_task. Activity Monitor doesn't allow you to kill kernel_task at all - neither as admin nor as root.

If you try to outwit kernel_task by using kill -9 0 or /bin/kill -9 0 as root you just kill yourself i.e. the first command kills bash (kill is an integrated command of bash) and the second command kills /bin/kill because in both cases the 0 is interpreted as me/yourself and not as kernel_task.

The man page for the system call kill (which is called by both kill and /bin/kill) explains that

If pid is zero:
    Sig is sent to all processes whose group ID is equal to the process group ID of
    the sender, and for which the process has permission; this is a variant of
    killpg(2).


This makes it basically impossible to even attempt to kill the process with PID 0.