Extremely important - but in the way that an actual manager sort is in RealJobLand. Lot of delegation, and the guys on the line (or in the cubes) are the ones who have to deliver. Manager's job is to put the workers in the right roles, and create a work environment where guys can do their best. And then there is being the public face of the team, and making sure management's vision and priorities make it onto the field. (so while nobody wants to lose, wins and losses are a very reductive way of looking at it).
Francona is a favorite of mine - but it is because, of all the great coaches/managers I know in sport, he most closely resembles what a really good boss looks like in the sort of world where most of us live and work.