Hello Paul,
You are describing an evaporative cooler, and yes they will cool the air that pass through them, and it can at first seem refreshing, but as you point out they humidify the air.
They are most effective when the relative humidity of the air passing through them is low, so it can take up more moisture, but after any prolonged use in a small space, the relative humidity of the air will rise, and the ability of the system cool the air diminishes. The air become very clammy, and it is debatable which is more uncomfortable, dry heat or clammy heat at a slightly lower temperature.
There dangers with these devices. The conditions in which they are used make the breeding grounds for bugs including legionella, which is why any self respecting H&S department ban them in industrial or commercial premiss.
Adding humidity to the air in a caravan will also lead to more pronounced condensation.
Personally I find dry heat to be more comfortable. Often just causing the air to move will be preferable to the clammy atmosphere so a simple fan may be just as effective in the long run.