I am sure it can be done. With a heavy barrel, reloaded custom rounds up to the desired velocity you need, there is no reason why it cannot be done.
Standard AK pushes the standard 124gr AK bullet about 2400 fps, if you can make a load to get a little bit hotter, say 2600 fps, it should reach 1000 easily. As long as you can stay supersonic at your intended target than you should be good to go.
The AK bullet is not that great of a flier, so another thing they might have done is used a special bullet that flies better. Some bullets do fly flatter (flatter = better) than others, but there is no reason why the AK platform cannot accept a better flying bullet similar to the 6.5 Grendel.