Does the Gospel of Grace teach that you can live ungodly to experience God's grace?
No. The Gospel of Grace does not teach that ungodly living is a way to experience God's grace. Paul calls that a slanderous report and says condemnation is just for those who claim believers say, "Let us do evil, that good may come." Grace is appropriated by faith, not by sin.
Les teaches that reconciliation has been accomplished for every person, and all they have to do is believe it, to appropriate it. God has every right to pour out His wrath because He has done everything possible to make salvation as simple as possible. In verse 7 Paul asks why he is judged as a sinner if the truth of God abounded through his lie to His glory. Even Saul of Tarsus, a religious zealot of Judaism, had to be told he was a sinner and undone. In verse 8 Paul rejects the slanderous report that he says, "Let us do evil, that good may come," and declares that the condemnation of those who say this is just. Les recalls a British theologian's commentary on Romans chapter 6: if the Gospel of Grace is not proclaimed as this book intends, some will accuse us, saying that if that is the way it is, then you are telling me I can live as ungodly as I want so I can check out the grace of God. No, that is not what it means.