Everyone's first reaction is to say no, but James Cameron was successfully sued by Harlan Ellison for much, much, much less on The Terminator. I actually recommend looking up that story, it's interesting to see how stringently intellectual property rights were defended back then as compared to now, as the similarities between Ellison's work and Cameron's Terminator is nowhere near as close as Battle Royale to The Hunger Games.
Also I believe the makers of "Parts: The Clonus Horror" successfully sued the makers of "The Island," did they not?
I think they *could* win, but that the legal costs/time expense would vastly outweigh any potential benefits. (Given how hard the Hunger Games Folk/Hollywood would fight back.)
I think the story line is different enough that Hunger Games could and would probably get away with it. Plus, like Morguloth said, the Hunger Games team has a looooooooot of money so.....