You can run without a leveller, but it's very difficult to maintain good control when near the surface. The faster the boat goes, the more difficul this becomes.
Keeping a submarine at periscope depth for any distance without a leveller is like flying an aeroplane 3" off the ground, with one eye shut. Some pilots might manage it, but it's awfully hard.
At very low speeds, static forces help keep your boat nice and level, once you get past a snails speed, without a leveller the boat will begin to porpoise.
Levellers work on a pendulum principle. Up until about ten years ago, this pendulum was either mechanical or fluid based. However progress means we can now use accelerometer chips. These use various methods, the most rugged of which is sensing a bubble of hot air inside the chip e.g. like a spirit level.
Levellers used to be quite bulky and expensive. Now they're tiny and cheap- not fitting one is a no brainer unless you're really cash strapped.
Depth controllers are a nice luxury. But I would say that 99% of model submariners I've met run without one. They use a pressure sensor (usually piezo based), which acts as a wheatstone bridge, and that feeds into a microcontroller which in turn controls the hydrovane servo (often the forward vanes, but you can hook them up to the rear vanes). These sensors are a lot more expensive than accelerometer chips, which is why depth controllers tend to be that bit more expensive.