No that's just a trait granted from the mythical creature his Zoan encompasses. Pirate Warrior 3 gave me some questions of how stuff is connected too but we should remember that it's just game material and not necessarily 100% in line with the show. But to answer I don't think so, the power of the phoenix is to revive so I think what's really happening is he is taking the damage but his Phoenix body destroys and replaces the damaged area so quick it looks like the "logia defense"
Btw how have you been enjoying the game? I've been liking it, it's a nice building block I think. People are being a little too hard, it's a bit difficult to get a rhythm going but it's a fun game and like most of these games it's about seeing the moves animated. I hope they put out DLC characters, it'd be fun to play as CP-9, Coby, Arlong, Dragon etc. Who are some others you'd like them to add?