Unless otherwise noted in the text of the rule itself, a special rule applying only to a character does not apply to the unit, and vice versa. Most special rules are there to represent specific skills or powers – you couldn't learn to shoot a longbow by standing next to someone who could, so why would you become able to perform a Killing Blow, deploy as a Scout, and so on?

On the other hand, many spells and magic items bestow special rules and other effects on units. In this case, everyone (including the character) in the combined unit will be affected.