No, ancient Egyptians did not use a written musical note system. We know what kind of instruments they had, but that's pretty much it. To get an idea as to what the music could have sounded like, we can look at Egyptian 'folk music' today and the style of the liturgical music of the Coptic Orthodox Church (which may be ultimately derived from ancient Egyptian religious music). But this would produce only an approximation. Music you hear in films are modern compositions.

Related question: when did this sound (I guess they're both variations on a minor scale with a raised fourth) first become associated with the middle east in western music? Stuff like Strauss' Dance of the seven veils from Salome, and Saint-Saens's Bacchanale from Samson and Delilah comes to mind, but are there older examples?