Olga N. was one of Alexei's godmothers, according to The Life and Tragedy of Alexandra Feodorovna by Sophie Buxhoevden. An excerpt from the book reads:
"His four small sisters, in short Court dresses, gazed open-eyed at the ceremony, Olga Nicholaevna, then nine years old, being in the important position of one of the godmothers."
Alexei had other godparents as well, but evidently Olga was one of them. I have never heard of Tatiana, Maria or Anastasia having any godchildren, though. But I think that it is definitely possible. Anyone else have more information?