Do the villagers ever succeed in the action they're attempting?

When walking around town I see villagers carrying tools like spades, bug nets and watering cans. In addition, I've actually observed villagers fishing and shaking trees. However, I've never seen them actually succeed in fishing anything up, or get anything from the trees they shake. They also seem to avoid fruit trees bearing fruits.

Do anything come of the villager's actions? Do they actually catch bugs, water flowers, or ever successfully catch a fish and get things shaken out of trees? And will the results be the same if the player tries to shake the same tree?