I would actually really like to see this. 343i says they want Chief to be less of a blank slate and to actually exhibit some real humanity... this would be a great way to do that.

Chief has just lost Cortana, his best friend / girlfriend / mom and possibly the only intelligence in the universe to ever truly understand him, and so it's only natural that he would bury his guilt under mountains of work.

I expect he will try to distance himself from Blue Team as well, since they don't understand what he's going through.