Basically. It's led to a a few nonsensical plot twists where he's alienated/ destroyed forces that would ally with or befriend him, but for the most part the intention is to show that he's just a really angry individual. At heart, he's the hero that the fans know him to be. The Gray Hulk's the antithesis of that- early on, he was the original Hulk incarnation; now, he's essentially an angsty teenager in the Hulk's body but with a lessened capacity to grow in strength.
As of recent events, people have gotten to calling this new version the Gravage Hulk or just PH/WWH Hulk. But he still has that urge to smash like his less-intelligent incarnation.