$680M is in the realm of a cash transaction for a hedge fund, and indeed, if you look at their SEC filing (below), this is an all-cash transaction. Expect aggressive cost-cutting from Elliot (BNs around me seem to be well staffed with lots of people standing around with little to do - so layoffs likely in the future) but the store itself should be able to survive.
http://investors.barnesandnobleinc.com/static-files/e605e233...
The cost cutting has happened in many places and if it continues, sadly, even a hedge fund won't be able to save it. Sure, lots of room to improve, and a mix of cut the bad and add the good will help. But don't fool yourself, retail is hard and B&N, the good ones, is real work. I wish them the best but it's a hard road.