Yes, but PP was right. The speeds at which molecules travel in thermal motion are so high that a bubble of heavy gas (relatively) soon diffuses freely into the atmosphere, especially with the assistance of wind and other disturbances. Of course, the short term effects can be more dramatic. For example, a lake of cool CO2 emerging from lake Nyos was able to flow down a valley, killing all at low levels, but sparing things on higher ground. Within hours at most however, there were no pools of CO2 anywhere; it has all dispersed, heavy or not.
Yes, He and H2 do not last long in our atmosphere relatively speaking, but that has little to do with buoyancy; their molecules diffuse through the atmosphere at thousands of metres per second, so sooner or later their bouncing takes them more or less randomly through the stratosphere, and in the thermosphere they get hot enough to exceed escape velocity. Again sooner or later they get past collisions with more sluggish molecules and leave Earth behind.
It is a statistical process, not buoyancy or stratification as such.
