Can you cook boneless skinnless chix from semifrozen?

Of course you can. Make sure to cook to the correct temp and you'll be fine. Poaching rarely dries out food just be carefull to watch closely.

Yes, you can do this -- Tyson actually sells frozen chicken breast portions which are supposed to be cooked from frozen. The potential problem is, as you noted, that the outside will be above temp long before the inside comes up to temp. If the breasts were halved before they were frozen, this is not much of a problem. If the breasts are whole, you may have some touch chicken by the time it is done.

Now that I think about it, seems the outside will be tough before that inside comes to the correct internal temp, so I'm running them under water first. Thanks.

It should be fine semi frozen as long as you get to the correct internal temperature.