I have no idea. I would not believe it myself, but I do feel noticeable difference/relief in eye strain when using on battery compared to connected to AC power. Not just in the new X1 carbon laptop, but also on my old laptop as well.
In my old laptop, which is the Lenovo T420s, I have also tested this (battery vs AC) and I also feel noticeable difference. In my old laptop, i have configured all advanced power settings to be exactly the same for on-battery and AC power (everything on maximum performance and max brightness), because the T420s laptop has PWM flickering, by putting maximum performance and max brightnesss (even on battery) it eliminates PWM. Even with almost every power settings identical for on battery and on AC power, I still feel the difference in eye strain.
Another mystery to solve in this whole eye strain thing.