I suppose that energy still has to go somewhere. Which place will warm up if Europe and North America cool down?
I suppose you could compare this to one giant heat pump, circulating a heat source to Europe and North America that makes life livable.
If the AMOC collapses, that heat will presumably stay in the tropics, and North Western Europe will cool.
It does after it's gone north along the US East coast yes, then it crosses over to Europe, but it's obviously not as hot anymore having dumped some of its heat into the US and the North Atlantic.
There's no current that goes directly from the equatorial regions straight up to the west coast of Europe.