Initially it was thought believed that they could/would be stopped but as stated, an AHB queen hatches 2 days before European queens do, so once one hatches, it automatically kills any and all other gestating queens in their cells before they can hatch, and takes over the colony. Just as an aside, the first European queen to hatch (no AHBs present) will ALSO kill any/all other queens in their cells.
Once they moved across the Panama canal, there was nothing to stop them continuing north until they meet the climate change (too cold) that would stop them. I believe colonies have now been found in areas that experience actual winter weather. That being the case, I think they are with us to stay. There's no way to eradicate them at this point. But we CAN learn to work with them and use them. We just have to be careful.
http://www.propacificbee.com/infographic/AHB/infographic.php Keep in mind this site is from 2012-2013 and bees had reached TN. They have spread further since that time.
In Panama, extensive studies have been conducted regarding the AHB's effect on local pollinators (honey bees as well as all other bee pollinators). As it turns out, the AHB's have actually benefited ALL of the other pollinators, including the European bee colonies. All seem to have learned to coexist and better pollination is happening across the board.