Although I have never dissected a Bike computer, I have used similar instruments in laboratories and here is how they work. The sensor has a coil in it called a Hall Effect sensor. When the magnet on the spoke passes the coil, it produces a voltage spike. The faster it passes, the higher the voltage. The slower it passes the wider the voltage spike. A stronger magnetic field (bigger magnet or moving the sensor closer to the magnet) will also increase the voltage. The computer has a frequency counter and an oscillator that produces a stream of pulses. When the voltage from the Hall Effect sensor's pulse gets high enough, it starts the counter. When the next pulse comes, it stops counting. By knowing the frequency of the oscillator and the number of pulses, it calculates how long it has taken to make one revolution. We input how far the bike goes in one wheel revolution so it is a simple matter to convert the data to speed.

Now, to answer your questions. If the magnet is too close to the axle and you are driving real slow, or the sensor is too far away from the magnet, then you may not generate enough voltage to trip the counter. If you move past the magnet real quickly, then the pulse may not be wide enough to start the counter. Modern electronics are very fast and so I would not worry about having enough time to trigger the counter. You are better off making sure you have enough voltage so mount the magnet near the outside of the wheel if you are concerned with the computer's reliability.

Here are some other factors not to consider. By moving the magnet outward, you are increasing the rotation momentum of the wheel ever so slightly which means it takes more power to get up to speed. The mass of the magnet is tiny compared to the mass of the wheel so don't worry about it. It also produced an unbalance force but again it is so small you can ignore it.