EK does have special arrangements at DXB for immigration fast tracks (if you book in business, first, or are a skywards member). However, depending on your routings this won't make a difference, as immigration circa 10PM to midnight at DXB is usually filled to the brim anyway. You have about 10 flights from Europe landing in a 45 minute period, not to mention flights from other Asian and African destinations. Even though I was on BA, they waved us through to the Emirates fast track counter anyway.