When cleaning my stove, can i submerge the coil elements?

The stove in my apartment is one of those old, olive green ones, that has coil elements (i'm used to the gl top type) I can remove them for cleaning, but can I put the whole thing under water? It would seem to me that they 'plug in' so is this really stupid to ask? I honestly never remember cleaning a stove like this before, so any advice would be helpful. Also this is the first time i don't have a self cleaning oven. I have heard it's easiest to take the door off to clean it, any idea how to do that?