All modern caravans, are now fitted with a power supply unit. This is designed to safely charge a leisure battery but it will also safely run many of the items in a caravan WITH or WITHOUT a battery connected.
These power supplies produce a smoothed and regulated output typically of 13.8V which is the standard voltage for charging leisure batteries and will not damage sensitive electronics unlike the simpler battery chargers fitted a few years ago.
These power supplies do have a limited current capacity, typically ranging from 12 to 16A depending on the model, so as others have said, its fine for running a few 12V lights and the water pump, but not for running a motor mover.
It is entirely possible to run a modern basic caravan without a battery, but if you use a lot of additional 12V appliances then the addition of a battery will help to maintain the supply when using the extra items.