Yes, Emirates is still due to get 340-500s (not -600s as far as I'm aware) and it is intent on using these on nonstops from DXB to the US. It is now 15 years old and has quite an impressive fleet - unusual in that AT THE MOMENT they are all widebody twins.
Topping the fleet is 3 773s (the third arrived within the last month), there are also about 7 772s. There also also 777LRs on order (someone else confirm?) It is due to get up to 22 A330-200s and boy, is that a nice airplane. The A300-600s and A310-300 are still there, althhough in smaller numbers and the airline will get rid of these in the next few years, as more 330s arrive. It is said to be looking for a narrowbody type - more than likely the 32X. Oh, and what's this I'm forgetting . . . some other Airbus type they have on order, a little bigger, well, than anything else! You know it!
It's a good airline, expanding quickly and knows its business. Good luck to them.