During the climactic battle between Hal and Parallax, Parallax grabs Hal and starts to feed on him. Parallax, being a creature that feeds off fear, would have some sort of fear-based component to the feeding process. He gets partway through feeding off Hal, and then Carol distracts him. Afterwards, Hal seems to possess much more powerful constructs, and skill with his ring is greatly improved. Did the partial feeding remove Hal's fear, making him a more effective Green Lantern?
It was discussed obliquely in bits & pieces throughout the movie.
Green energy comes from willpower. Yellow energy comes from fear. A Green Lantern's ring is limited only by the limits of the bearer's willpower and imagination. Courage is having the willpower to face/overcome one's fears and continue on.
So, ultimately, it's not lack of fear that makes Hal Jordan a strong Lantern, it's an abundance of courage.
IMHO, it's this characteristic that seems to make him more capable than most Lanterns at dealing with yellow-energy crises, as well.
(Copied from comment to answer as suggested by Keen.)
Fear is not limitless, and cannot be removed. It's a biological response to stress, and we can make as much of it as we need. It can be suppressed, but not eliminated.
River Tam in Firefly aptly demonstrates this during the series, as the portions of her mind which allow her to suppress fear and other emotions have been disabled (she gets better in the movie).
Hal does, indeed, feel fear. It's likely that Parallax's feeding actually INCREASES the fear in his victims (for a time) as their stress levels continue to rise. It would only weaken as they did.
Hal was able to suppress his fear because Carol was in danger and he put her there. She distracted Parallax KNOWING that she was dead meat if she got his attention, just to save him. His sense of responsibility tempered by his need to protect her helped him overcome his fear.
No, he is not fearless. He is able to find ways to overcome his fears. There is no such thing as someone having no fear. There are only those who succumb to it and those who find ways to subdue their fears.