Unless they fix the issues that caused TOR to lose sixty to eighty percent, or more by this point, of its customers in the first place. Something I'm pretty confident EA is no where near willing to pay for. I just don't see them letting people play some of the game for free is going to give them any more than a speed bump in "actives." I'll keep my fingers crossed but, personally, I'm pretty doubtful.
If TOR was a Turbine, Trion, or even Blizzard game, I would be more hopeful that any profit would go back "into" the game. However, its EA we are talking about here and I get the feeling that they've already written it off.