Your challenge to unbelievers to put their money where their mouth is, so to speak, is both biblical and wise. Many are happy to talk religion and philosophy, but as soon as it dawns on them that if Jesus is Lord, there are certain expectations, they back away, excusing themselves like Felix (Acts 24:25)!
I would say yes: virtually every skeptic or agnostic or "seeker" or atheist who became a Christian embraced the challenge to be willing to live out the faith. John 7:16-17 is also appropriate: Jesus answered, “My teaching is not my own. It comes from the one who sent me. Anyone who chooses to do the will of God will find out whether my teaching comes from God or whether I speak on my own." This doesn't mean telling them to "just believe" so that they will believe -- that would be irrational. Rather, we must be willing to believe if we are ever going to understand the truth. We always have a choice.
Yet God will not force himself on us. I like the way Pascal put it: "there is enough light for those who desire only to see, and enough darkness for those of a contrary disposition." (Il y a assez de lumière pour ceux qui ne désirent que de voir, et assez d'obscurité pour ceux qui ont une disposition contraire.) Like Goldilocks' porridge, the amount of evidence God has made available is just right.
Our approach to unbelievers should combine intellect and heart. That is, answer his or her questions, expect your friend to investigate scripture, emphasize that the Christian faith is rooted in history, and will not be uprooted by a difficult question or supposed contradiction. Yet also challenge your friend to enter Jesus' thought world, and to try to keep his commandments. It takes some genuine experience of seeking and finding to light the fires of faith.