I am not an engineer. But I have done coursework in EE and Microcontroller programming.
Shouldn't damage the computer, that much I can be certain of. The sensor is probably a Hall effect or simple magnetic switch. The worst that could happen is you can't get the sensor to ever think that the magnet has passed the wheel till you move it away. Well unless you somehow magically break the sensor with the magnet, but I've never seen that.
As for how the computer will read it, that will depend on a number of factors but primarily how the guy who designed the thing programmed it. I've programmed microcontrollers with speed readings and there are a few ways to do it. One is to measure the off time between hits, like you say. The other is to measure the hits per second and display that. The ease of doing each would depend on the hardware you're working with and is puerly academic for the discussion we're having. I'm willing to bet however, that some computers work based on the former method, and some on the latter (Low end sigma sports, in particular...)
If it's measuring the time between hits, it again is an issue of programming semantics. You could reset the counter as soon as the 'switch' is hit on, or wait for it to be switched 'off' before resetting the counter.
I won't comment on the dynamics of the magnet sensor itself with a big magnet, because I can't pretend to know about those things.
<-- This dude loves magnets though and I bet you could ask him. Might take a little while to get an answer however.
Long story short, give it a try, see if the reading's accurate.... I'd test at all 3 speed ranges, 0-10, 10-20, 20-30.