I don't think you'd need to change your story for it, because it doesn't change the facts for baby Natasha, but the reveal of the Red Room's ruthlessness towards Natasha was a big deal for the audience: you could hear people respond to it with a few gasps.

If you imagine the program as established before Natasha arrived, then this graduation ceremony thing might have happened to others before her, and would be something the adults would know, and might talk about. If you imagine Natasha as one of the first kids in a new program, then this might not even have been decided yet. Either way, the film didn't give any specific places or dates, so.

It's a background detail that most readers will know. It won't affect your story, but it might be cool to mention (or not; there'll be lots of references in fic about adult!Natasha.)