dude, this is so weird, I've been considering doing a thread on this. My point of view is yes, he is.
From an objective standpoint, his "mission" is crazy. Obsessively devote yourself to a one-man war on crime to the exclusion of your own happiness and normal life. Not to mention, dressing up as a bat and being a vigilante is a pretty stupid way to fight crime. Why doesn't he run for office or use his financial resources to combat the social causes of crime? His method is the most inefficient way of doing it, and then to add to that, he refuses to kill, which means that he willingly lets mass murderers like the Joker get more chances to kill, in contrast to his stated mission of making sure others won't have to go through what Bruce did as a kid.
I agree with the Joker in "Batman Beyond: Return of the Joker" -Batman's still a little kid crying for his mom and dad. He never moved on and got over their deaths. He let their deaths DEFINE his entire life, how is that not crazy?