Hi,
Here's a great tip for defrosting a freezer, I've done it and it is soooo quick.
Use a steam cleaner with a nozzle attachment, and point at the freezer (switch it off first!). Honestly, it is amazing how quickly the frost and ice melt. I think I did the last defrost in 10 minutes.
Now you do have to have the place prepared, because the water comes out pretty darn quick! But I cannot reccommend this method highly enough. It is still a pain, but a relatively quick one now.
To the OP, no, I would never leave the door closed on a fridge that was turned off. Also, the smell of the water coming out of the freezer on your kitchen floor would be awful.