From The game manual:
If the abandoned buildings are not bulldozed, they will be inhabited again after a minimum of 4 weeks of in-game time. Burned down buildings need to be bulldozed to make room for a new building.
So no, you don't have to demolish abandoned buidlings, but demolishing has the following benefits:
- Avoiding 4-weeks wait.
- Improving the land value around that location.
You have to demolish burned down buildings, though.