I'm pretty sure it counts. I helped someone get 100 visitors by simply leaving and coming back and it worked, so I'm guessing it works for dream visiting as well
Yes. When I dream I take just the amount of bells that I plan on dreaming. Pick random and leave as soon as I arrive. If the town looks nice I'm mark the town DC down and visit later. Once the bells are spent I know how many dreams I've done.
One night while watching TV I picked random and I got sent to the same town 3 times. It just kept repeating the top ten on the list.
Left the dream suite and Mr. Badge guy was waiting with my badge.
After I'm done random ones I dream towns that are on my list. Usually spend about 30 minutes on each of those towns.