Thing is it works without those things in a great way. It's currently well designed, and very versatile. Gradients and reflections would be uneccessary in this instance, and giving it 'depth' as you say would completely change the style of the piece and give it that web 2.0 look, which I personally am not a fan of and doesn't generally work for versatility in logos anyway.
Can be a nice look on the internet though, as long as it keeps the logo in the same style and feel as the non gradienty reflecty version.