Does it matter if you talk to people with your gun out in Fallout New Vegas?

It doesn't effect your disposition in most conversations. However, it does effect your outcome in certain quests. For example, if you draw your weapon during the fight at the train station while completing the "G.I. Blues" quest, the NCR will shoot you on sight. Also if you openly wear a weapon or draw it at one of the strip's casinos, a fight will break out. Hope this helped!