If you break into Evelyn's house before meeting her in the House of Healing, you trigger the following things: The murder questline is advanced to the point when Evelyn has run away. You are told to find her hideout. The dying men in the House of Healing beds are not there anymore, and as such you cannot choose who to save, and more importantly, you do not get teleported to meet the crazy imp guy and all that entails.
You can proceed with the main quest in the sense that you've "solved" the crime and now must go and find out where Evelyn is hiding, but you haven't found out about the Void, got fast travel, or found the Hall or Heroes location (I'm a little uncertain I've remember the name correctly, but you know what I mean).
