Well, let's see. It costs 500,000 dollars to get into Sushi High Roller (450,000 after your first try). Let's go through all of the battles and see how much you can make with Amulet Coin and Level 3 Prize Money O-Power.
Amulet Coin doubles prize money gained, and a Level 3 Prize Money O-Power triples it. This is x6 the normal amount of money gained.
Battle 1: $28,080 reward - $421,920 down
Battle 2: $28,080 reward - $393,840 down
Battle 3: $28,080 reward - $365,760 down
Battle 4: $28,080 reward - $337,680 down
Battle 5: $62,400 reward - $275,280 down
Perfect Reward (25 Big Nuggets): $250,000 profit - $25,280 down
Now, here are all of the same calculations but with Happy Hour Inkay in play as well, boosting the prize money gained to x12. (Exclusive to Japan without trading)
Battle 1: $56,160 reward - $393,840 down
Battle 2: $56,160 reward - $337,680 down
Battle 3: $56,160 reward - $281,520 down
Battle 4: $56,160 reward - $225,360 down
Battle 5: $124,800 reward - $169,200 down
Perfect Reward (25 Big Nuggets): $250,000 profit - $80,800 gained
So, yes, it is a money sink only if you don't have Happy Hour in play. However, you can get some good experience out of it as all of the Pokemon's levels are 65.