The relationship between the characters should have some effect (on the characters and other party members), but I don't know if or how it may change dialog later in the game, etc. Presumably any story or dialog changes would be relatively minor (given the amount of work vs the relative little benefit that would provide, since most people don't replay games many times). Henchmen or companions may leave your party if there is too much conflict (proposed as an example during the kickstarter IIRC), but the two main characters are presumably going to get to the end of the game together.
