I predict it wouldn't be as fun as it might initially sound. NPC dialog is part of level design just like all the rest of the level it occurs on. With few exceptions (such as roguelikes), random level generation tends to produce bland cookie-cutter levels; I don't see why dialog would be any different. The reason it's fun to talk to NPCs in a game like Chrono Trigger or FF7 is because someone put the work in to make their dialog interesting and relevant and fun.

Where I could see it working better would be for e.g. newspaper headlines in a grand-strategy or SimCity-like game. When you do something crazy like have Lichtenstein conquer Western Europe, it could be funny to have some auto-generated commentary on said crazy state of affairs.