Very short answer, no.
So how sufficient is the Bible to govern a society composed of diverse religious adherents and non-believers? We already know that the Bible has not been sufficient to yield a unified church. Now it’s supposed to give us a platform for cultural and political cogency and coherence in a diverse and religiously free society?
The objections to Frame and Leithart are not simply empirical or based on United States law. They are also theological. Appealing to the Bible as a norm for non-believers places those who don’t believe in an odd situation, at least according to theology that stresses the anti-thesis. How are those hostile to God going to submit to GOVERNMENT based on the Bible? I have asked this many times and I’m still lacking a decent answer, one that actually does justice to the Bible’s prohibitions against idolatry and the United States’ legal toleration of what some of its citizens consider idolatry. Another question is this: doesn’t a proposal for the Bible’s sufficiency as a rule for culture and society mean ultimately that only believers will GOVERN? After all, if fallen human beings cannot understand the Bible aright without the illumination of the Spirit, then only the regenerate may GOVERN because they alone have the discernment to apply Scripture to society and culture.
Perhaps some people are so busy trying to "get upstream" and "influence culture" they haven't bothered to think through how they should handle things once they get in those positions? Perhaps this is because the odds of this ever happening are near zero?
The lesson is that 2k (aka SCET) is really more faithful to Reformed teachings (which are biblical) than are 2k critics’ constant charges of infidelity and deficiency. Those who think the Bible sufficient to GOVERN culture or society must either form a political body comprised only of church members or they must cut and paste biblical teachings to make it fit a religiously mixed society. Either way (Massachusetts Bay or liberal Protestantism), we’ve been there and done that. Time for 2k’s critics to come up with their own proposals for GOVERNING and transforming culture that are not blinded to their own insufficiencies.
Of course I know there are people who would say that two kingdom theology would not allow someone to stop Hitler. The Roman church didn't stop Hitler and it doesn't seem to have always propounded two kingdom theology. As Mark Noll noted, lots of evangelicals who would have agreed we should all use the Bible couldn't work out the same answers to the questions of race and American slavery and weren't listening to the Papists and Jews who actually had some ideas on how to field that because they weren't Christians or weren't real Christians. There have been some people who are upset about the secular state we have and I'm not suggesting there aren't things to be unhappy about, but the thing about trying to get MORE religion into civil society is that you can't be srue that YOUR religion is going to be the one that makes it. As various people fretting about, say, the Islamization of America are discovering, just because you want "God" back in America doesn't necessarily mean it's going to be a foregone conclusion that your god will get more public endorsement. It's why liberal secularists consider conservative evangelicals and Muslims pushing for sharia to be on the same moral playing field.
Not that I'd consider myself a liberal on theology or politics but Hart's got some points. His book From Billy Graham to Sarah Palin was an informative survey of evangelical approaches to politics. It's worth checking out just for the chapter called something like "The Search for a Useful History".