That might be a glitch. But I'm sure that all companions have some sort of specific skills (which means, Veronica is skillful in Unarmed, Boone is skillful in Guns, and Arcade is skillful in Energy weapons.).
And in New Vegas, All companions have scripts which makes them do something when they are in some situation that they wouldn't like. For example, Boone would not like it and try to break the relationship with you when you earned reputations with Caesar's Legion, and Veronica would put the guns down and say something that she will give up this weapon and switch to her own unarmed weapon somehow when she uses them in the fight. So, Arcade would do the similar way, just like Veronica.
In your situation, I think Arcade put the chainsaw away from his inventory cause he isn't skilled in melee weapons, or he wouldn't like to use them.