Back-to-back centuries (with a significant sleep in the middle) shouldn't be referred to as a double century. But if the sleep duration is much shorter than normal, like only a 60-120 minute nap, then maybe. I have several rando friends who do those nutty 1200km rides in under 90 hours with just a few 2-4 hours sleeps, and it's considered one ride.
I prepared for my first double century by riding a century every other weekend, prior to the double, as well as a back to back 150 mile ride. But the double century was also a trainer for the triple century I did 2 weeks later (325 miles in 24 hours, with no sleep). The best preparation I did was to get professionally fit to the right saddle!