The way this will affect your high end is this:
With no high end beyond 12k, you'll boost the high end heavily when mixing because you won't be able to hear it on those monitors. In other words, you'll be compensating for the lack of high end on the monitors. Then, when you take that mix and listen to it on speakers that have a full frequency range, like practically anything else on the planet, the high end will be SCREAMING.
This is not the way you want to mix. You need at least a somewhat accurate representation of the frequency range from maybe 30hz to 20k. Yes, it won't be flat all the way across that, but you certainly need something above 12k!