Most likely not. I've done it in the past without incident. However there is a chance you get in a hurry, open the door, and pull the card before it has quite finished a write. You'll lose the last "take" and can also wind up with a corrupted card.
When you shut the camera down and wait until all displays have gone black the camera has had a chance to close any and all open files. This is always the safest way and these days I always power down before removing or changing media cards.
And it is also a good idea to shut the camera down before doing a lens change. A few owners of C300's have found themselves with a dead camera after a lens swap. It is supposed to be OK but the potential is always there.