Yes and no in that order :)
Yes, every district will have a Boss (mostly girls, but sometimes not - as in the case of The Chief) but choosing to recruit, imprison, exile or kill won't usually have an effect on the story, beyond altering people's reactions to you and your actions (execute a lot of people and you may earn the "Monster" title, or recruit everyone and become known as an "Incubus"). There's 40+ districts in the first map alone so not every leader can have an impact.
That being said, there are exceptions, and when you come across a story-critical boss, the game will let you know they're special in some way.