Even in water saturated with calcium carbonate, there is a constant exchange of solid material with ions so the surface is constantly reforming. This is similar to the effect one finds with ice in a freezer -- eventually the ice surface goes from smooth to jagged even though the total amount of ice may remain the same. However, with well-made plaster this is a very slow effect which is why such plaster lasts for decades. pH is probably a more important factor after saturation of calcium carbonate; temperature is also an important factor. Higher pH and lower temperature both slow down the rate of this surface exchange.
If the saturation index were consistently high, there would be a slow buildup of scale while if it were consistently low the plaster would slowly dissolve, but for well-made plaster these effects are slow. Ideally, one wants the saturation index at 0, but onBalance has shown that for well-made plaster no degradation is seen until the saturation index gets into the -0.7 to -1.0 range so having it be in the -0.3 to +0.3 range should have the plaster last for quite some time. However, for poorly-made plaster, the degradation rate is faster if the saturation index isn't at 0 so if you are unsure of the quality of the plaster then it would be best to err on the side of saturating or slightly over-saturating with calcium carbonate.
The calcium scale covering the plaster surface would probably prevent any natural erosion or aging. At some point in time, one could sand or acid wash the plaster surface and expose the original (smooth) surface again.