No, I don't think so. It's a fun alternate reality. I personally am fascinated with Russian history and I still love the film Anastasia. There are so many historical inaccuracies in the 1997 version that I wouldn't know where to start.
#1 Anastasia was 16 when the Russian Revolution started, not 8. Which would make her about 26 and not 18 when we first meet her in the film.
#2 Anastasia's grandmother moved to Copenhagen where she was originally from, not Paris.
#3 Rasputin did not have anything to do with the deaths of the Romanovs (although his relationship with them did provide for hostility with the people of Russia). In fact he was dead before they were.
#4 The story is based on the woman who called herself Anastasia, but even by 1997, DNA test results proved that she was not in fact the real Grand Duchess Anastasia. It was already known as fantasy.
#5 Many believe that Anastasia's body was recovered in the 90s while her sister Maria and brother Alexei were the two bodies found in 2008. But due to the amount of damage done to the bodies and skeletal remains, it is hard to pinpoint which body belongs to which grand duchess.