Does a near infrared AF assist light work with contrast detect autofocus?
The AF assist light is mainly red. Maybe it reaches beyond the visible red spectrum and into near infrared because the filters are cheaply made, but since most cameras have IR-filters, its effect would be negligible.
However, I think that for CDAF, a multi-spectrum-light (i.e. white) would work better than a red light source, since red and red will have roughly the same contrast. It will help nonetheless, though.
Does a near infrared AF assist light work with Canon's dual pixel autofocus?
Again: It is not really NIR and the sensor has an IR-filter. Canon's Dual Pixel AF is a form of phase-detection AF that sits on the image sensor. I think that the AF assist light will work better with PDAF than with CDAF, since in principle, it does not rely on contrast in the scene too heavily.
Would NIR light help a traditional PDAF sensor?
See "Why don't most cameras use infrared for focusing?". In short, NIR does not get transmitted through lenses all too well, its longer wavelength means that it is less intense, and it does not feature the same focus points as visible light.
How to tell whether something is red or (near) infrared?
The prefix "infra" is the opposite to "ultra" and roughly translated means "beyond". Beyond what? Beyond the visible spectrum! Maybe you can see wavelengths longer than red - there are people that can see ultraviolet light, so why not? However, think of the average IR remote control: You cannot see if it works or not with the naked eye.
Why red and not white, blue, ...?
I have yet to find the study that I read about this some years ago again, but red has been found to be the least distracting/blinding color. In some European countries (and I think across the world, though I cannot speak authoritatively for places I haven't been to), traffic enforcement cameras were only allowed when they became usable with red flashlights, as you can even use them at night without blinding the driver.
 Wikipedia states: "The assist light (also known as AF illuminator) "activates" passive autofocus systems in low-light and low-contrast situations in some cameras. The lamp projects visible or IR light onto the subject, which the camera's autofocus system uses to achieve focus." I have yet to find an IR light source on a recent (that is: younger than 1990) flash, however.