My school was pretty similar - we didn't called it getting dropped though, just lavaliered. It was the step before engagement for us and it definitely meant a lot - so not done very often, but often enough that we knew what it meant. We would also have a candlelight for it, as other chapters do (but ours are for friendship, lavaliere, engagement, pregnancy - that way alums can have candlelights in their chapters as well). Being lavaliered allows the woman to wear his letters and know some of the traditions also - it's as if the fraternity is adopting her into their brotherhood as well. I know TKE used to drop the guy in the pond after they would serenade the girl. We had one girl get lavaliered by a TKE at our chapter meeting and we did the candlelight for her as a surprise (at the request of the boyfriend) so he came up behind her and blew it out! Then the brothers filed in and sang to her, and then carried him out to drop him in the pond. Crazy college kids....
It was really sweet to watch though!