Q: Do you think a melody alone can give a story (like an instrumental) and would not just need to be both lyrics and the melody?
A: instrumental melodies are found all the time accompanying pictures or video. and that is one of the most powerful combinations there is. but perhaps you were assuming that it is not video- or picture-assisted. and then i realize you didn't even specify if it has chords or not. but if it has no chords, no visuals, and you are also not allowed to go anywhere, do anything, or see anything, while listening to it, ...... then i think the answer is still yes you can still tell a story