What exactly do you mean by "overwatered"?

If your plants are in pots with proper drainage holes and planted with a reasonably fast draining potting soil mix, a one time watering is not likely to cause any serious issues. But if you repeat this too frequently or your potting soil is excessively water retentive and takes too long to drain well, you could be on the road to root rots. Same if you let any containers sit in saucers of water or in a cache pot that has no drain holes.

byw, watering your containers until the water runs freely from the bottom, allowing them to drain thoroughly and then not watering again until the soil tests dry IS the recommended way to water most containerized plants, inside or out.

It is really the quality and ability of the potting soil to drain quickly and thoroughly that determines how serious a problem overwatering may be.