Reality has performed relevant experiments on a number of occasions. I don't think that anyone has deliberately performed such experiments, but you can argue that they have been done inadvertently.
Remember Mount Pinatubo erupting in the Philippines, in 1991? When it erupted it injected a few megatonnes (20-odd) of SO2 in the atmosphere, close to the equator. This was identifiable as a plume for several months, during which time it completed circling the Earth (the near-equatorial source was important in this). Over the next year or so, it disperses both north and south, and became dispersed into the general atmosphere.
Inadvertently, the nuclear Test Ban Treaty monitoring system performs (performed) similar experiments on an irregular basis. The detonation of a nuclear weapon releases short-lived and longer-lived isotopes of various elements into the atmosphere (even underground tests ; the detonation tends to make holes in containment structures), which disperse. Depending on the state of the weather and the size of the territory in which the explosion occurred, it can take several days for the plume to reach a detector, but invariably they do. (Embassies can have detector arrays on the roof ; not that the host country particularly likes this, but they don't want their embassies searched either.) Probably the best known exmaple of this was in tracking the nuclide plume form Chernobyl across eastern, then northern Europe in 1986.
Both of these types of data sources indicate that the diffusion and dispersal of point sources of gas in the atmosphere takes a matter of weeks on a national scale, and only a couple of years for a point emission to become globally mixed. The most persistent anomaly would be with a point source at high latitude, when it might take a half-decade or so to be dispersed into the opposite hemisphere.
I hope I can learn if there are any models or measurements that show how narrow and/or quickly can effects of greenhouse gases be measured.
Why look at models when you've got relevant experimental data?