they does happen when you nearing the cities and when you’re leaving too, but you have a better chance that you won’t get them. I’ve been experimenting with deliveries for a while and “Along the road” have a MUCH higher chances too happen when you are really along the road. I did it even with the same mission through a save game. Tried road at first – got myself kicked badly – loaded – marched through forests and mountains and got to dest safely without any combat including the event one…
EDIT: Oh, and yeah there is delivery event that could happen no matter where you are going, one with the cursed box, that spawns ghosts and skeletons and they could be deadly on the start w\o fear immune. But it happens pretty rarely through two ~300 Days companies I seen it twice or so and I was building reps so I did every mission they threw at me at the time.