The most likely scenario that would result in the "entire developed world suddenly magically disappeared" is a nuclear winter, though. Such an event would drop global temperatures by a lot more than 2 C, nullifying the problem.
Please don't give politicians ideas.
Everyone thought that "The Wall" was a joke, and yet...
This NASA link says CO2 stays in the atmosphere for hundreds of years: https://climate.nasa.gov/news/2915/the-atmosphere-getting-a-...
And this site: https://www.skepticalscience.com/co2-residence-time.htm
explains that while the individual molecule CO2 hangs around the atmosphere for 3-4 years, it's then merely exchanged with one in the oceans (or maybe one in a rotting tree).
On this study: https://scholars.unh.edu/cgi/viewcontent.cgi?referer=https:/...
on page 4 (shown 25 on the page), you can see the box model of the global carbon cycle. Halflife refers on how long the a CO2 molecule spends in a given box.