Do air conditioners work better when they have a filter in them?

Air conditioners, whether a window unit or a central unit, MUST have a filter. Otherwise, dust, lint, dirt, pet hair, etc. will clog up the cooling coils. The cooling coils are damp, and the dust and dirt, etc. will stick to them, which will result in the fan not being able to blow air through the unit. This will very quickly result in a unit that is damaged beyond repair.