Statistically speaking, highly unlikely ... on the other hand, if the quality of the games continues to improve as it has through games 1-4, then the answer must be: could be! 
Anand/Carlsen Immortal Game
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fastcache wrote:
Will Anand/Carlsen 2013 produce an immortal game?
It seems unlikely, because immortal games are very rare. If a few players have one or two in an entire career, what are the chances they will have one in these 12 games? Combine that with that fact that immortal games often require entering into massive complications that can't be 100% foreseen, and it seems even less likely.
Has there ever been an immortal game duing a WC match? The only one I can think of that might be in that category is the 6th game in the Fischer-Spassky match, and while it's considered amazing and one of the best games ever, I tend to hear "Immortal" used more for tactically breathtaking games, like Kasparov's game against Topalov, so maybe there aren't any true immortals in WC matches.
It's fun to dream. You're probably right that the "reckless" abandon that is likely necessary to bring this to fruition is probably not suited for the World Championship. But then again, is there any better setting?
I think it could. Depends on a couple of things.
Go into game 10 or 11 and it is all tied up, and Carlsen REALLY wants it this time around, it could produce an immortal game.
Or, goes into game 11 or 12 and Anand is down 1 game, that could also produce one.
A slightly different question is - in todays era of preparation and coaching will we ever see an immortal game again?
They have already look at this one. http://www.chessgames.com/perl/chessgame?gid=1693032
This is a true Masterpiece and it is hard to see what Black did wrong
Will Anand/Carlsen 2013 produce an immortal game?