As a group, their mission seems simple: to play early music at as high a level as possible, and while being as historically informed as possible. It seems that they need not do much in the way of "show" in order to maintain their audience, since the clientele they play to know what they're after in a concert.
So it would seem that in the continuum of Artistry vs. Showmanship, they lean far toward Artistry, without any gimmicks or pranks onstage. But with a target audience as informed and learned as the group undoubtedly draws, this seems less necessary than if they were trying to appeal to a wider range of listeners.
Their website can be found at http://www.aam.co.uk.