Does a Democratic Iran Mean a Nuclear Free Iran

Would a democratic Iran abandon nuclear weapons?

Jennifer Rubin criticizes Secretary Clinton's speech on human rights:

This is what passes for “smart” diplomacy. But it’s revealing. Never does it dawn on the Obami that human rights, support for democracy, and regime change might actually enhance our objectives and afford us a solution to the problem of an Islamic fundamentalist state’s acquisition of nuclear arms.

I'm not an "Obami" (whatever that is) but I would be interested in seeing this assertion substantiated. On what basis should we believe that if Iran's Green movement were to prevail, it would mean the end to Iran's nuclear ambitions? Put another way, if the Green movement had succeeded in forcing the Supreme Leader to hold another election and Mousavi won, would Rubin and company believe that the threat from Iran's nuclear program had been substantially mitigated?

UPDATE: Daniel Larison makes a good point:

Most Iranians are not preoccupied with foreign and security policies, just as most people in other countries are not, but if they believe as Iranian nationalists that building up their nuclear program is a matter of national right and pride they are going to continue backing their government as it pursues this. If Iranian nationalists see their government attempting to act as a regional power, enough of them are probably going to support it regardless of the character of that regime to make changing that policy politically difficult.

(AP Photos)