In the last stretch of One Piece's pre-timeskip, Luffy wound up having to run away from most of the arc big bads, since he'd gotten to a point where he couldn't keep up to the power curve.
The exception to this is Boa Hancock, who he managed to pacify without ever having to actually fight her.
So, if they had come to blows, could Luffy have defeated the Empress of Amazon Lily? Or would he have been forced to run from her too?