The Hibernate problem only applies to external solutions (like LiveDiscs, Bart-PE etc.).
Not quite, because JkDefrag can process unmounted volumes, like I just explained. I think the hybernation problem can also apply to other volumes than the system volume, if system files have been relocated to that other volume. For example the pagefile.
By the way, JkDefrag has a build-in protection for this problem and when it detects hybernation on a volume it will refuse to process that volume. But it is best to avoid the problem altogether and never use hybernation in the first place. See the JkDefrag homepage, the "How do I defragment C:\hiberfil.sys" question, for instructions on how to disable hybernation forever.