Law isn't a swordsman. He only uses his sword to compliment his Devil Fruit ability, seemingly similar to Fujitora.
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I doubt if this contest would be anything but a warm up to what would proceed in Dressarosa. These contestants, excepting perhaps Jesus Burgess, should be fodder for Luffy. Seeing as it were the way his punches and kick flung Hody Jones hither thither, the question is, how much damage might the crowd suffer if he chooses to go heavy on his opponents.
On another note, I wonder why people think Bartho's barrier power might be a problem to Luffy? Isn't Haki supposed to negate the use of devil fruit powers? Unless Bartho's Haki is stronger than Luffy's, which I very much doubt, he would be blown away with any Haki infused attack.
In my opinion, Luffy is absolutely being underestimated. For someone who lost his brother the way he did and seeking to avenge his death, it would be offensive to think he would reappear without the power to match any enemy he apprehends. Even Raleigh shed a happy tear in anticipation of the glory that would come Luffy's way knowing indeed that he now had the power to go all the way.
I don't think so.
Law one-shot Vergo with his Devil Fruit, even when Vergo was in full-body, Armament Haki. Haki allows the user to "touch" Logia users when they're in an elemental form.