Though I would advise you to put off reading the rest for a year or two, or you will have a torturous few years (maybe more) waiting on the next.
Personally I don't think he'll finish the series before he dies.
That is one reason I am choosing not to finish the series. I think GRRM has lost inspiration to finish it.
I picked up AGOT and ACOK just before the ASOS hardback it the shelves. I then read ASOS and it was the best book of the series yet with some shocking developments resulting in the deaths of some main characters that I had been invested in over all three books.
Then I waited, and waited, and waited. When the fourth book hit the stand 5 or 6 years later, I didnt bother to read it. And then I heard reports and read reviews that GRRM has introduced loads more characters and POVs (ahem... like Jordan), there is a ton of filler and fluff while the story itself inches forward at a snailpace (ahem... like Jordan), and alot of pointless redundancy (ahem... like Jordan).
Now, when GRRM originally wrote the fourth book it had too many pages and he had to go back and re-edit the whole thing into two books instead of one. That is why it took so long but in effect probably one of the main reasons quality isnt up to par with the first three books. The series hasnt recovered from these delays and the re-edit of book four. And plus, maybe GRRM has lost inspiration to finish the series properly.