They will get wet, twice. Luggage are almost always transported in small chains of relatively flat carts pulled by a motor vehicle. Then, a conveyor belt loads them into the plane as works move each piece from the carts to the belt. As some comments say, the carts sometimes are covered, which I have seen but it was not complete coverage, so water will still reach a number of luggage items.
As you can see this gives them plenty of opportunities to get wet, including while being loaded on the cart, while in the carts and while on the conveyor belt. The process is the same at arrival except in the reverse order.
Very few suitcases are completely waterproof but how much water gets in varies. To ensure things like sensitive equipment stays dry, most people use pelican cases. A cardboard box will certainly allow water infiltration quickly, even more so than other materials, particularly because it is absorbent. Some airports even place luggage on the ground, either while waiting to be moved or for passengers to pick up themselves (I've had to do this several times in small airports).
Plastic wrap is a good idea and the kind that wraps several times over it quite effective. There is no guarantee that it will absolutely stay dry or not be pierced but, even if it does, you will get much less water in than with a cardboard box. The other option which I use more often is to pack the contents in giant ziplock bags. Again, its not 100% effective but works nearly every time.