It's a plausible theory but, while there's been a slight slowing, it turns out to be wishful thinking.
First, so far there's little impact: according to the US National Ocean and Atmospheric Administration, in the year to February 2009 global emissions grew at a rate of 2.28 ppm per year. The total concentration of CO2 equivalent gases in the atmosphere now stands at 463ppm. Co2 is at 386ppm. (See http://www.esrl.noaa.gov/gmd/ccgg/trends/index.html#global)
Mark Hughes of Climate Risk argues that, because of what's happening with other factors, the economic downturn and GDP deterioration is not likely to get atmospheric CO2 levels down in the future either.
While there's an approximate relationship between global GDP and emissions from energy, this doesn't catch the full greenhouse gas picture by any means and can be misleading.
Essentially, emissions from sources other than energy (e.g. agriculture, land-use, land-use change and forestry etc.) are still growing. Forestry and agriculture alone account for about 31% of global greenhouse gas emissions.
Plus, atmospheric greenhouse gas concentrations are effected by global carbon sink efficiencies and these have recently been reported to be deteriorating. On top of that positive feedbacks are starting to come into play (e.g. release of previously stored methane from permafrost and deep sea floor deposits).