Without aux battles, yes .. definitely.
Chapter 13 is unforgiving, especially if you're unprepared. If it helps, there's a guide on Youtube by Mekkah showing how to complete it on all routes, very helpful. (Really fun on Hard, awful on Maddening.)
I would like to add, I am certain that this is the case since on my playthrough, as soon as the reinforcements moved into the range of the Death Knight, he began to move.