Burning gas/oil mix actually creates more pollutants than just gas, the problem is it creates more irritating emissions. I don't see why it wouldn't work but it might be slightly less comfortable.
From a article I saw in the Washington Post
"The two-stroke engine has developed a reputation as an environmental hazard. Because the engine lacks an independent lubrication system, fuel has to be mixed with oil. More important, about 30 percent of the fuel the engine uses fails to undergo complete combustion; as a result, the engine emits a number of air pollutants. Carbon monoxide, nitrous oxides and hydrocarbons escape from the engine in large quantities. Everyone knows the acute effects of carbon monoxide, but the other gases are equally worrisome. Both nitrous oxides and hydrocarbons contribute to smog formation. Hydrocarbons can be carcinogenic"