Nope, 'Poohbah' is the name of one of the characters in 'The Mikado' by Gilbert and Sullivan. He had a vast array of titles, such as Lord Chief Justice, Master of the Buckhounds and Groom of the Back Stairs, as well as the handy catch-all post of Lord High Everything Else.
Sure, but where did Gilbert and Sullivan get that name...hmmmm? (I'm just playing with the name; it struck me as sounding like PBUH.)