The real hole in my supposition is can she carry Minnesota for Romney and will he need that state? If you can answer both those questions in the affirmative then I think I might be on to something.
I do not think it is about any state. It would make much sense for Romney to pick a conservative woman as VP. McCain did it and did much better afterwards, he was even leading in some polls before he self destructed his campaign. Romney knows that most conservatives would never vote for him alone just like most conservatives would not have voted for McCain without Palin. I think if he picked Bachmann it would be about getting conservatives on board and not about any state or region.