The science on Atlantic Meridional Overturning Circulation shutdown happening is a bit iffy, not in that it is bad science, but rather that it requires a pretty specific set of circumstances, a meltwater pulse at just the right time, that isn't that likely to happen, with global warming. Way more likely to happen is a slight weakening in the circulation, which just slows the rate of warming for a few years. Anyways, North America would not be that heavily affected, it would be the western shore of Europe that would face the bulk of the effects.

It definitely wouldn't kickstart the next ice age, if that is what you are implying. The Younger Dryas occurred with a much weaker Milankovitch forcing, kicking off an feedback loop of cooling temperatures is more or less impossible even if the AMOC shuts down completely under current conditions. Worst case scenario for an AMOC shutdown is temperatures dropping in the UK and the Norwegian coast by up to 10 degrees, elsewhere in Europe by less than half that, and not really affecting North America much as prevailing weather patterns are from the west here. It definitely would not stop global warming.