I think you might be misunderstanding the nature of input lag.
Input lag in overly simplistic terms is the delay related to how long between the monitor receiving a video signal from the computer and actually processing/displaying it.
Refresh rate wouldn't affect input lag any more than the space of time between two frames. If you are asking if a higher refresh rate would affect the single digit ms because the frames are compressed, the answer is yes it would be a few single ms faster simple because more frames are being delivered per second.
The real question is whether there is any meaningful ADDITIONAL delay caused by extra processing in the monitor's control board.
In the case of the Crossover, almost certainly not. It should be virtually the ideal case because it is nothing but a single input DVI controller, without even so much as an on-screen display.
My point here, is that your question isn't really a necessary one. The screen by it's nature will have supremely low input lag because it doesn't have any unnecessary processing going on internally, and it also happens to overclock to a nice refresh rate which by the nature of running a higher refresh rate and compressing frame times lowers input lag a tiny hair more.
As a contrast to the very fast Crossover, or my previous very fast BenQ 2720Z, I have a nice 47" 1080p TV that I used for several years for gaming, but discovered the up to 75ms display lag really doesn't cut it for any kind of competitive gameplay. So yes it matters, but this screen will be among the best you can possibly get for input lag.