|Data from CDIAC. Asterisks notes dips with multiple possible causes.|
While this is by no means a comprehensive scientific analysis, it is a very interesting and telling observation. If you look at the global fossil fuel emissions data, all of the major disruptions to energy and oil use in the past 60 years caused carbon emissions to drop or level off. Annual emissions would later continue to rise at a rate similar to that before the disruption, but the total annual emissions would not "catch up" to where it "would have been" without the disruption.
The recent world financial crisis appears, on the surface at least, to be an exception. Carbon emissions stopped rising in 2008 and 2009, but rebounded so strongly in the past couple years, that emissions have reached the level to which they appeared to be headed, presuming linear extrapolation, before the crisis.
I'll let you argue why: whether it is the nature of the crisis, the rise of China's economy, etc. Regardless of the cause, the effect points to the potential naivete, not to mention the questionable morality, of people thinking or hoping that economic slowdowns will 'naturally' limit carbon emissions and save the world from the dangerous impacts of climate change.