The only reason he worked with Arbiter was because Johnson ordered him to. Have you read the books? Master Chief killed four ODSTs because they wouldn't leave him alone, and you think he doesn't like people around him because they might get hurt? Chief rarely even talks, when he does its usually sarcastic or cynical. Chief doesn't trust very many people, but those he does trust have earned it, Keyes he knew since he was six, Johnson and the Arbiter fought beside him, Cortana was given to him by Halsey, and has been with him for years. So she's the equivalent to the ghost in Destiny. And Hunters have those. His speed and reflexes also demonstrate his Hunter side, as he was one of the fastest of the Spartan IIs. Another note one could take is his battlefield problem solving, making things work when it's just him, and his constant infiltration into unknown territory. He was originally designed for one purpose, to be the ultimate killer, Spartans were created to hunt down and kill insurrectionists. That was his purpose, to hunt. So yes, he has many qualities that would make him a Hunter.