From the time she was a child, Natalie Wood's mother filled her head with stories about how they were related to the Romanovs. (Not so, although they were Russian.) So Natalie Wood did have a lifelong interest in things Russian, and in fact I remember watching a program she hosted about the Hermitage.
Our family had subscription tickets to the Ahmanson Theater in Los Angeles. In the spring we learned that one of next year's productions would be Anastasia, starring Natalie Wood as the Grand Duchess Anastasia/Anna Anderson and Wendy Hiller as the Dowager Empress. That fall, however, Natalie Wood drowned while she and her husband, Robert Wagner, were staying on board their boat, moored off Catalina Island.
Remember that Ingrid Bergman was not terribly young when she starred in the movie; a youthful looking actress, as was the case with both Ms. Bergman and Ms. Wood, would not have difficulties being convincing in the Anna Anderson role.