Or dead. We can't know for sure at this moment, seeing as there's no defining proof yet. So, let's say that he DOES die. These are my predictions as to how things would play out after his death:
1. Luffy goes batshit. SH declare absolute war on Donquixote pirates, and Dressrosa goes bazonkers.
2. Luffy is in shock, and the plans of the Straw Hats immediately fall to ruins, with Doflamingo's victory seemingly in the bag. Then yada yada, they save the day somehow.
3. Flashback occurs of Law's life for a few chapters, then we see Dofla attempt to kill Luffy himself.
In any case, Law dying seems way too much like Ace dying. Everyone loves him, he dies fighting a madman, Luffy goes into shock then comes back to save another day. Boring.
Now, what would happen if Law were to stay alive, on the other hand? My predictions:
1. Doflamingo is prevented from finishing Law off somehow, by someone, and then (possibly Zoro and Kinemon, or one of the Heart pirates) swoop in and save him last minute, keeping him safe for the rest of the arc while he's incapacitated.
2. After flashbacks, something distracts Doflamingo, and someone rushes to save Law, see above for rest.
3. Doflamingo seemingly finishes him, but turns out Law's vital organs aren't in his body, and the only thing threatening him is his blood loss. He hobbles off to get organs, etc.
Regardless of what happens, Law is going to be incapacitated for most of, if not the rest, of this arc. After all is said and done, we may not see much of Law for a while, should he still be alive.
Is he alive? Or dead?