Was Gurudeva (Yoganandaji) an Avadhut or an Avatar? I have some doubts relating to this, as Gurudeva spoke of his previous incarnations, as William the Conqueror, and also as a diamond. But I feel I've read that Sri Yukteshwar named him a "Premavatar". Also, I remember Swami Kriyananda saying (in one of his recent Satsangs, I guess) that even William the Conqueror was an Avatar. My facts might be wrong, but please do clarify.
Yes, Yogananda said he was an Avatar and his life proved it in many ways (and keeps proving it in the hearts and lives of his living disciples).
It is true he said that he remembered all his past lifetimes, as all liberated beings do, in human incarnations as well as non-human forms such as animals, plants, and minerals – and in that “list,” he included the lifetime during which he played the part of William the Conqueror.
He also stated that he was Arjuna in the time of the Mahabharata. There were other specific past incarnations he mentioned, too.
No, it was not Sri Yukteswar who named Paramhansa Yogananda a Premavatar, “an incarnation of divine love.” It was Yogananda’s most advanced disciple Rajarshi Janakananda, who gave his guru this title.
As to your question about whether Yogananda was actively functioning as an Avatar when he was William, he obviously had a very different mission at that time – different from the one he had as Paramhansa Yogananda in our times. But that wouldn’t have made him any less of an Avatar. It was just a unusual sort of role he needed to play in that lifetime.
He said that he has come again and again and would continue to do so as long as there are those in need of spiritual salvation, or to correct or make some sort of needed changes in the way things are going on this planet. That’s what Avatars do.
His mission as William might outwardly appear to be very much less spiritually oriented, but it was necessary for the evolution of our planet at that time.
If you are interested in learning a lot more about this fascinating subject, please read the book Two Souls, Four Lives, which explains about William and his son Henry, in much greater detail.