Although I'm personally not a big fan of the Lady Luck dressphere (apart from the Bribe ability, which is just plain awesome for some really useful items), winning or not the tournament will affect your story completion % - you won't get 100% if you don't - so you should really try. Only thing to do really is to save after your second tournament win and reload the game if Shinra starts using his core sphere 1 (what a major pain, LOL). From time to time, he doesn't use it at all - I usually have to reload the game 5-7 times, but it's worth it