Possible, sure. Arguably required as an indie/small team. But if your aim is AA/AAA industry it's shooting yourself in the foot. Those industries seek deep specialists more than generalized knowledge. Maybe a director can benefit most, but you don't become a game director through that route. They promote that in-house.

On the indie side, a generalist indie needs less of what a big game needs. You probably don't need a graphics programmer at all for an indie game, for example.