That would make no sense as that would mean the final switcheroo twist isn't a twist. If David gets a scar from fighting Walter, then the audience would know it's David in the last part of the movie, and I'm fairly sure from the leaks that we're not supposed to know this is David.
The more probable outcome is that Walter gets cut at some point and that David must cut himself to look like him.
Unless it happens off screen, and the audience has no way to tell whether David or Walter gets cut in the face... then yes, David could get that scar from an off screen confrontation with Walter.
My money is on the first option