Can an EVA kill it's pilot through harm caused during battle?
After doing some reading on the Evangelion Wikis, I stumbled upon an article that answers this question.

An Evangelion can kill it's pilot with shock from the injuries, and therefore Central Command has to watch the sync rate between the pilot and the Unit to ensure that the pilot does not die during combat, as was nearly the case with Unit 02 and Asuka vs Zeruel.

Source --> https://wiki.evageeks.org/Evangelions (See The Effect of Damage to the Evas upon their Pilots)