If I'm reading this right, you're basically trying to put together an evaporative cooler (swamp cooler) . The idea being that heat will be transferred from the laptop's bottom, through two sheets of aluminum foil, along a steel plate, to a pool of water with cotton balls in it to accelerate the evaporation process. On a theoretical basis, yes the idea will work. I can see several problems with it though.
1) I doubt you'll get much heat transfer through the bottom of the laptop. Laptops are designed to vent heat into the air via the heatsink and fan. If you were to somehow replace this heatsink with water cooling and attach that radiator to your steel plate (or just dunk the radiator in your water), it would be a lot more effective. Just because the bottom of the laptop gets hot doesn't mean it's a good place to draw heat. Temperature is caused by the combination of heat generation and heat removal. If you have low heat removal (like the bottom of a laptop), even a low rate of heat generation will lead to high temperatures.
2) The layers of aluminum foil will severely degrade your heat transfer. The CPU's heat spreader and heat sink are not perfectly flat, so people use thermal paste to fill in any air gaps that form when you mate them. You're proposing putting two layers of aluminum foil on a steel plate, which creates three non-flat contact surfaces which will be full of microscopic air gaps. Thermal paste is a pretty lousy heat conductor, but air is much much worse so it's preferable to have the gaps filled with paste.
3) If you can get it to work, yes you'll have condensation. Any time you cool something below air temperature, you risk condensation. Assuming it worked, the evaporation would lower the water temperature below ambient air temperature. That in turn would cool the steel, which cools the aluminum foil. The foil being below ambient air temperature and having a large surface area would cause water in the air to condense onto it. How much depends on the temperature differential and the humidity of the air. So the foil wouldn't be very effective at keeping your laptop dry, since the more effective it is at cooling, the lower the temperature of the foil, and the greater the condensation from the ambient air.
4) This is a rather complex contraption. Probably overly complex. You can basically achieve the same thing by buying a swamp cooler and pumping its outflow air (which will typically be 5-20 degrees cooler than the ambient air, depending on relative humidity) into the intake vents on the laptop. The laptop's fans will then blow it over the heatsink, and the cooler air temp will cause a greater rate of heat transfer. The problem being that you're blowing humidified air into the laptop. The heat of the laptop should help prevent condensation and corrosion (heating up the air increases the amount of water vapor it can hold, thus increasing evaporation and reducing the risk of condensation - how a hair dryer works), But if there's any part of the laptop which for whatever reason is cooler than this humid air, then water will condense onto it.
The temperature reduction of the swamp cooler will also depend on the ambient air temperature and humidity. The higher the ambient humidity, the less effective the cooling. Swamp coolers are very effective in hot, dry air like in a desert. They're pretty useless when the humidity is high. Also, a few cotton balls in a pool of water isn't going to generate much cooling. You'll need at least a fan, preferably blowing through the cotton (rather than just over).
http://home.howstuffworks.com/home-improvement/heating-and-cooling/swamp-cooler.htm