Based on current trends (Arena in 2004, Daggerfall in 2009), I'm guessing Morrowind will go free to play in 2014, in commemoration of TES's 20th Anniversary. But as to the topic's title question, it's not likely.
If they release a free game in 2014, I'm sure it will be http://www.elderscrolls.com/battlespire/, which was originally released back in 1997. And then there's http://www.elderscrolls.com/redguard/ from 1998 and after that maybe Morrowind. So in 2024, 13 years from now?
So yeah, I don't think Morrowind will be released for free anytime soon. Modern Windowses can still run Morrowind without any issues (which can't be said about the DOS games like Daggerfall which need DOSBox to work) and they are http://store.steampowered.com/app/22320/ even though it's 9 years old, so they still get money from Morrowind.