Regarding the safety issue:
There is A LOT of near IR light in regular sun light - so I think our eyes are well equipped to handle that part of the spectrum.
A sunny day has much more IR light than a LED array in an indoor environment...

On top of that, I know of a number of car manufacturers (big ones) who are working on integrating driver's eye detection for safety application in their vehicles (identifying that a driver is drowsy). They use active IR LEDs to illuminate the drivers face and eyes, and from what I understood it is safe for the eyes (if not they should expect major lawsuits...)

I work in computer vision and have experience with active IR illumination - and I think that the major issue here would be the "noise" coming from reflections on the face and other surfaces. reflected light tends to reduce in intensity much faster / closer than illuminated light, so in order to get a reliable signal the sensitivity of the camera would have to be increased - introducing more reflections from other surfaces.

It might work, but it's not a given thing...