This topic and the related one in your other question had 2 aspects: phenomenological and terminological ones.
Meteorological and chemical precipitation are different phenomena.
- The former is the water phase change from gas to liquid or solid, that is (almost) independent on air presence, with vapour saturated pressure criteria, usually considered in context of falling on Earth surface.
- The latter is based on limited solubility criteria of a compound in a liquid.
Solubility of a compound in liquids depends on this compound, the liquid and temperature.
The maximum compound concentration in a gaseous phase depends on this compound and temperature, but does not ( almost (*) ) depend on the kind of gas, its pressure or presence at all.
As gases do not dissolve compounds, but are just bystanders, we cannot speak about dissolving and precipitating from them in chemical sense.
Precipitation is applicable to solids with difficulty, as processes of dissolving and precipitating are mostly kinetically frozen.
Diffusion process in hot solids is definitely considerable, OTOH it is extremely hard to observe it. But it does happens and is observed in some circumstances, like steel or alloy processing.
(*) Almost: Saturated vapour pressure slightly depends on the overall pressure by a generic way. Compound phase equilibrium implies equality of compound chemical potentials in both phases. Liquid chemical potential slightly increase with total pressure, what is followed by slightly increased saturated vapour pressure.
This effect may be dramatic near liquid critical conditions, as seen for $\ce{N2O + O2}$ mixture Entonox, where the mixture is at the storage conditions gaseous, but pure $\ce{N2O}$ would condensate.
See also SE article and Wikipedia.
Other then this, gases do not affect the equilibrium vapour pressure, but may cause equilibrium disturbance by side reactions, turning vapour molecules into different compound or a compound adduct.
The extreme example is putting liquid ammonia and hydrogen chloride at $\pu{-40 ^{\circ}C}$ side by side. Both vapours would never reach equilibrium due forming solid ammonium chloride.
Molecules moving by free flight in gases is a well known fact, which you can easily find and would not ask others to find it for you. For flying in vacuum, molecules need not other molecules flying nearby.
E.g. the mean free flight path of molecules in air is typically 70 nm, what is 2-3 orders more than molecule size.
Note that I was serving in the Czechoslovak army as an enlisted air force meteorologist in 1989-1990.