Yes CO2 is heavier than O2. The proof is seen when you place dry ice, which is frozen solid CO2, into a container of water, the dry ice will "boil" turning from a solid into a gas. The gas which is seen as a fog (as in many horror films: the bubbling potion with fog flowing out on Dr Jeckyl's desk or as fog in a cemetery laying low on the dirt) will flow over the container's side and will flow down to the lowest point such as the floor. Eventually the CO2 gas will expand and dissipate into the room and the fog will disappear.
So – yes the CO2 will remain in the carboy neck for a bit of time but will want to expand to fill the room. I don't know exactly how long the CO2 remains there. I do know from using dry ice fog in theatrical situations, that the CO2 fog will dissipate, if it is not replaced, in about 2 minutes