Yes, I already have done it. I didn't mind it because I was able to get new, popular villagers in town while doing the cycle to sell on here or just give them away. I had 6 dreamies when one moved out. When I finally got her back, I had accumulated over 20 million bells from selling the villagers that moved in during the cycle and I also happened to get another dreamie in that time. It was a win-win for me.
Well, actually, I did the 16 Villager Cycle, but not to directly get back my dreamies, but it's been a long time, and villagers have been moving out, as well as those pesky villagers that randomly move in on you when you had 8 villagers. I also need to get rid of those villagers to make room for my dreamies. Let me warn you though, the 16 Villager Cycle is long, especially when you have to be careful not to make dreamies move out. (I'm blaming you, Bam and Simon) I have experienced dreamies moving out without telling me, and I just replace them. (That includes you, Flurry, Freya, Bob, Pheobe, Fauna, etc.) Because of all that cycling, I was able to get back Fauna, and I completed my dreamies list.