I would say it depends on the bonded pair. Most of them I've seen did not need to be adopted together, and would have done fine if separated. People do anthropomorphize animals sometimes and feel bad about splitting "pairs" up, but its better for the dogs in the long term because they will get adopted quicker if adopted out one at a time.
We have a bonded pair at FOHA right now named Puddle and Toot. I've posted some pics on here before, they are border collie mixes, but Toot is about two sizes smaller than Puddle. They sleep in one dog bed together, they can often be seen playing together, and you will see them grooming each other. Its so cute. They have been separated before when Toot had to go to the vet to get neutered, and Puddle did seem a bit lonely, but they would adjust fine if they had other dogs to play with in their new homes. They'll be adopted out together though, because they're just too darn adorable to separate.
One other bonded pair that comes to memory was one FOHA had a long time ago. There were three little dogs we got from a hoarding situation and they lived in a run together. One of the dogs, a beagle, was adopted and the other two were honestly, very sad.
We kept those two together, they were very bonded. They were two males, their names were Brownie and Scooter. Brownie was a brown beagle mix, and Scooter was a sheltie mix. They sure were two peas in a pod.
