No, that's definitely the wrong way to look at it, because a non-believer without Faith can have more works in Christ than all those of Faith put together, and it won't be enough to enter into the Kingdom of Heaven. One must... have FAITH, regardless of works.
However, what did Jesus say about treasure and one's heart? Wherever your treasure is, that is where your heart will be. And that means if you truly have Faith, then you will naturally have works to go along with that Faith. Likewise with the race analogy, you don't just claim to be a race-car driver with only filling out a race application form; you actually participate in the race.
Those against this understanding usually point to man's false Hyper-Grace Dispensationalist philosophy. That system by men is deception, because it promotes the idea that once one believes on Lord Jesus Christ, they have never have sin again, and never fall away. But their falling away and continuing in sin is exactly... what that Hyper-Grace system promotes! They don't watch theirselves for sin, and don't repent of sin, because they are told they cannot sin anymore because of their Faith on Jesus Christ. In that sense, that false doctrine is saying that doing iniquity doesn't really matter, because Jesus has already covered that.
And that is exactly the example Lord Jesus gave in Matthew 7 about those who will say, "Lord, Lord" on the day of His future coming, and He will tell them, "... I never knew you: depart from me, ye that work iniquity." (Matt.7:23)