I don't think so. After all it would still be about history. An own thread could be opened for a "movies' historical correctness quiz". However, actually I don't really care whether it is to be put in the Brain Food or the Silver Screen Forum.
In that case anyone taking part should post a list of all the movies about US history he or she watched and remembers, so we know which movies can be asked about...
If we open an own thread for it, we should expand it to include all history movies and not just those about American history which would rule out movies such as Braveheart, Titanic, Gladiator, the Battle of Britain etc.
Either way, I think we need a new question in this thread.