I would say no, if you have in mind the kind of dynamic process we have in a saturated solution which has a bit of undissolved solute at the bottom. In that case, dissolved solute is constantly coming out of solution, but undissolved solute is dissolving at exactly the same rate. In this dynamic state of equilibrium, there is constant activity but no net change.
In a supersaturated solution all of the solute is dissolved. However, for some reason there is more solute dissolved than should be possible under the conditions of the solution (e.g., temperature and amount of solvent). If even a little bit of undissolved solute were present, all the extra solute would quickly come out of solution (precipitate).
In the video you can see a demonstration of this in a supersaturated solution of sodium acetate.
A supersaturated solution of sodium acetate is poured onto a plate with some sodium acetate crystal on it.The dissolved solute quickly precipitates and forms a column. Near the end of the video the solution remaining in the beaker rapidly solidifies as the rest of the solute precipitates.
If I remember correctly, this solution was made with 50 g of sodium acetate trihydrate and 5 mL of distilled water, heated until all the sodium acetate was dissolved. It was then allowed to cool to room temperature, at which point it was supersaturated, and very unstable. Several attempts were made to pour it, but the solution quickly crystallized as it did near the end of this video. The video shows the attempt which was finally successful.