Yes HotrodPrincess, the corydoras will stay at the bottom. This question reminded me of something very important. They have barbels on their mouths to sift through sand for food. That is soething I didn't think to mention before suggesting them. If they are kept in a tank with gravel, sadly their barbels will get warn down which leads to death. I had mine with gravel and was told this very same thing. I thought mine looked fine and kept them in the gravel anyway. Then, sure enough, found one dead. Poor thing had no barbels! So, I changed from gravel to sand, and the younger ones grew their barbels back, but the older ones never did.
Just something to keep in mind.