We already have a model of an atmosphere-stripped Earth at hand, it's called Mars. Essentially, the loss of air on Mars meant more things didn't happen any longer than did happen. Erosion and corrosion processes caused by the air -- and by fine particles carried by the air-- largely stopped with the loss of a thick atmosphere, effectively freezing mineral deposits. As a result, explorations of the Martian surface may be used to identify areas that were exposed versus those that were protected (as if by a body of water).
For example, we may look at this answer at Space Exploration Stack Exchange, which summarizes the minerals found at various depths in the Gale Crater on Mars. Note especially the relative concentrations of mafic rock and iron oxides; the former is converted to the latter upon exposure to an oxidizing atmosphere. We see that the upper reaches, which likely would have been exposed when Mars had a thick atmosphere, still have the iron oxides produced by oxidation of the mafic rock, whereas the mafic matter below which might have been protected by a lake has remained largely intact.