There's actually special dialogue with several of the NPCs and at the start of quest missions if you don't go to Shooter Street until you get all members in your party, at least for base game characters. I don't think it applies to DLC characters since all the quests are base game (I think). The dialogue itself probably isn't anything special other than some additional characterization but it's interesting that Dandylion added it. Like it's neat that Giselle has dialogue at the start of the Yasha hunting missions even if most people are going to be doing those missions long before they get Giselle.
So putting off the quests and going through mission repetition hell could be worth it if you want to see those little easter eggs.