Well, as u suppose yet, it will be able to drive them. But well, "be able to" is few specific.
If you have no other amp and you use your ipod or your PC as source, of course the D3 is a very good improvement using de HD600s, but it wont really take out all the juice of them. A desktop amp is required for that (or a soooo expensive portable one, then you can get the same results spending less if you buy a desktop amp, because HD600s are not portable).
I had a D2 Boa, so i cant suggest you any headphone which have special synergy with D3, but searching at the forums i think you will find something.
If you like your shures and D3 but you like a better headphones for your house, and size doesnt matter, go then to the HD600s or something similar. If you have no more budget at the moment, you will enjoooooy much your HD600s + D3 combo. But in the future, if you save some money and you can buy too a desktop amp, then you will improve more your sound
Generally speaking, for a good headphones like HD600, Beyers or AKGs in this price range, always its required a good desktop amp to really take out their max. But this doesn't mean you wont love the sound of HD600+D3.