No, the MAP system still works just not as exact. The tables don't change just the variables in the equation.
It will see the change because the MAP system will sense a change in pressure and temperature and therefore extrapolate the higher air density.
If the cold air system actually works then it would deliver cooler air to the engine. Lets assume that the manifold pressure stays constant, then it would still indicate to the PCM that the air is more dense because it senses cooler air.
So both systems work. However, have your temp sensor, or your MAP sensor, or your tps go out on your speed density car and the thing will amost not drive at all!
Go out to your MAF system and unplug the Temp sensor, or the TPS, and the thing will still run almost perfect but with a check engine light.
Or, assume all your sensors are working but the MAF is not. Then the MAF system will be able to revert to a speed density system through extrapolation of manifold pressure. It will still run reasonably well.
Go out and try it, unplug just the MAF and then start the car and watch it will run pretty good.
In fact, that is one way to tell if you maf is dead and giving bad signals. You can unplug it and start the car. If the car runs better then you need to look into MAF related issues like vacuum leaks, bad mafs, etc.