Oh certainly they would, though I suspect the ratios are different. Mohammad was running a theocracy within his lifetime, so all the compromises and practicalities that were needed to actually govern. There's still a large amount of tradition that has to be applied, but you can talk about the Islamic way to govern much, much more concretely than the Christian way. Which if you believe in moral progress is a bit of a problem with Islam, but not one I'm going to dwell on when talking about societies that would be better off following the Koran more closely.

And incidentally, your point is somewhat opaque but I believe you're taking that Gandhi quote to mean the opposite of what he meant. That is, it isn't that politics does influence religion but that politics ought to be influence by religion.