I am not an expert, but I do have an opinion.

I think no.
Flamboyant blades do have more cutting surface than a straight blade of equal length. However, I have yet to see any compelling evidence that this has any practical effect on inflicted damage.
Perhaps the psychological impact is the primary advantage.
While perhaps not popular in the west, flamboyant blades did exist (two-handed swords and, even some rapiers).
I think they are harder to make than a comparable straight blade, and the absence of any significant advantage makes the effort not worthwhile.