Now let's say that when God asked Noah to do the whole ark-building thing, Noah said no. He did, after all, have the free will to do so, and a loving God wouldn't force him into anything, even if it meant sacrificing the entire human race so that Noah could have a choice.
So Noah declines. Humankind is now screwed.
God's not stupid. The person He picks to continue the human race would not refuse to obey Him. If there were nobody on earth who would be willing to obey Him, He would probably be justified in destroying everyone and starting over.
But in answer of your question, God could 'force' Noah to do His will. I just don't think He would.