The bridge isn't screwed down, just the posts. The bridge pivots against the posts on a "knife edge". It's the tension between the springs & the strings that holds the bridge in position, if you remove the strings it is possible on some floyds to pull the bridge away from the posts. If you were to remove the springs also, the bridge would just fall out, that is why Floyds can be such a pain to set up correctly because any change to the strings, action, spring tension has a knock on effect to something else.