Residence times of greenhouse gases are on the years to centuries timescale. The economy tanking was a blip in the rate emissions were added to the atmosphere, but the net balance was still positive. And even if it wasn't, a single year of net zero emissions would make a near negligible change to the existing inventory of greenhouse gases, which is up almost 50% over the highs of the past 800k years. There would be a detectable drop in methane (half life of 10.5 years) but not too much for CO2 (hl of 100+ years).

Getting to net zero isn't going to substantially reduce the amount of greenhouse gases in the atmosphere or stop warming in it's tracks, it's just about limiting how much higher the temperature is going to get (at least for the short to medium term).