Does the meridional overturning circulation slow down the temperature increase from global warming?
The short answer is 'yes'. Earth's response to climate change is closely coupled to the deep ocean's uptake of heat and $\ce{CO2}$; the ocean is by far the biggest sink for excess heat (~90% of the excess heat absorbed by the planet goes into the ocean, the rest largely goes towards melting ice sheets/glaciers).
The ocean is also a major sink for carbon.

How effective the ocean is at absorbing heat/$\ce{CO2}$ is closely tied to rates of deep water formation, that is the densification of near surface ocean water by surface fluxes like cooling and evaporation, which then sinks and doesn't come back to the surface for centuries or even millennia. The major deep water formation regions are the Southern Ocean and the North Atlantic. The sinking of North Atlantic Deep Water (NADW) is the northern part of the 'Atlantic Conveyor' (the term sometimes colloquially used to describe the AMOC).

A slowdown in the AMOC, therefore, wouldn't just impact regional climates in N. America and Western Europe, but would also reduce the deep ocean's uptake of heat and $\ce{CO2}$, and by consequence cause a greater increase in surface temperatures.