Are there any such documented cases? I would think that level of cognitive indirection is beyond most 3-7 year-olds.
Taylor and her colleagues found that 77 percent of these children said “yes” when asked if they had a pretend friend, and 40 percent spontaneously remarked at some point during the interview that they were talking about a pretend friend. The children offered statements such as, “Her is a fake animal,” “I just made him up in my head,” and “He’s not in real life.” Only one child was adamant that her invisible friend was real.
https://www.psychologytoday.com/gb/blog/growing-friendships/...
(Personal example: I deliberately lied about not understanding how to do long division just so I wouldn't look too clever in front of my peers - I kept up the pretence for several months.)
edit: To directly answer your question: I don't know, and that's part of my point.
Audience. A fake imaginary friend is a prop. The child sees imaginary friends are desirable and performs as if they have one. If there is no audience, there is no imaginary friend.
A bona fide imaginary friend, on the other hand, should be more likely to be addressed when the child thinks they’re alone.