Personally? Yeah, but not True Neutral. I think he is more Chaotic Neutral, maybe Neutral Evil, but definitely Chaotic Neutral.
We already know that Belkar isn’t Good since that Good Effecting spell didn’t work on Belkar. He doesn’t seem to show any type of traditions that he is devoted to follow himself, just basically what passes his fancy at the moment. So Lawful is out too.
So there are technically 3 alignments that I can see Belkar being: Chaotic Neutral, Neutral Evil, and Chaotic Evil. But I can’t see a good reason why Chaotic Evil character would ever join a party of Good Adventurers, especially with a Lawful Good person.
So by that thought process, I say he is Chaotic Neutral. Doesn’t give a shit really about anyone else, is ok with killing and violence, likes to fuck with people, can still join organizations to get better stuff (the party and the Barbarian Guild) and can still do good deeds when he feels like it.
I can see people arguing he is Neutral Evil, but the idea that he isn’t evil, but still is refusing to out his alignment to Miko just to fuck with her is something I can see him doing.