The answer must be a contingent yes. Feminist philosopher and Harvard professor Jane Mansbridge explored in a 1999 article the question of whether blacks should represent blacks and women represent women. She argued that "descriptive representation", or representation by people who, in some way, look and sound like their voter base, is good in certain contexts.
There are two particular implications from Mansbridge's research that should make us pause before throwing Bachmann out with the bathwater.
First, there are occasions in democracy that lend themselves to descriptive representation. Descriptive representatives can, according to Mansbridge, communicate to their voter base in a way others cannot. They also force us to deliberate on issues specific to their identity as a representative.
Second, descriptive representation can potentially recast underrepresented groups as "capable of ruling". Whatever Bachmann's politics, her presence as a serious presidential contender helps American society see women as potential political leaders. This, in turn, enhances the democratic legitimacy of a group historically excluded from high office – women.Full article: 'Should feminists back Michele Bachmann', The Guardian, August 25, 2011