I know how to tune and adjust spring tension and all that on a Floyd Rose, but what are the drawbacks of not having the bridge level with the guitar? Does it screw anything up?
Yes, it screws up intonation.
You won't be able to go an equal distance with dives or pulling up on the strings, it would also cause intonation problems. But above all it would mostly just make it look like you have no idea how to maintain a Floyd Rose.