No.
I abhor the final conclusion that Calvin arrived at.
If a parent holds to the doctrine Calvin concluded, then when his child reads scripture and says he wants to seek God and His mercy, then the parent can only respond, "You don't have a choice in the matter. You might be destined for hell, and there's not a darn thing you can do about it".
Sounds harsh.
But that is exactly the conclusion Calvin arrived at.
I think this speaks to much of the misconception of what Calvin meant. He did not say that man does not have a choice in the matter. There is far more to the story then that, and that is not the conclusion Calvin reached, rather the conclusion many reach about what Calvin meant.
It deserve more thought. So let's look at your statement from that of Calvin. "If a parent holds to the doctrine of Calvin and his child reads scripture and says "I want to seek God and his mercy, then my response is, "great, you can count yourself among the elect."
But I would also say this. In the bible .......(Note: I've pasted the rest from another site)
1 John 5:13 (New International Version)
13 I write these things to you who believe in the name of the Son of God so that you may know that you have eternal life.
This means that we are able to know that we are saved by the Lord Jesus Christ. But sometimes, we have our doubts and we wonder. So how do we know if we are elect. There are two ways a person can know that they are one of God's elect. The first deals with doctrine and the second deals with practice. 1 Cor. 2:14 says, "But a natural man does not accept the things of the Spirit of God; for they are foolishness to him, and he cannot understand them, because they are spiritually appraised." The natural man is the unbeliever. So the word of God is telling us to unbelievers cannot receive in and believe in the spiritual truths that lead to salvation. The spiritual truths include such things as Jesus dying for sin, Jesus being God in flesh, Jesus physically resurrected from the dead, etc. An unbeliever can understand the concept, but an unbeliever does not accept them and received them. So, if a person who claims to be Christian acknowledges these types of spiritual things, that is a sign of his regeneration. Only regenerated people are saved. The second thing to look at is the person's life. Christians seek to abandon their sin and to war against. Unbelievers don't do that. Only Christians are worried about spiritual issues about being right before God. Christians are the ones who, because they are saved and regenerated, have a repentance from sin and the change of life. So, we would see that Christians would be people who would avoid lying, stealing, etc. Unbelievers don't worry about their sin and unbelievers, those who are not regenerated, don't war against their sin.
So, though we cannot look into the heart to tell if someone else's saved, we can look into our own hearts and see if we affirm the basics of the Christian faith, those things which are discernible and believable only by Christians. And, we can no that we are warning against sin, seeking to do away with it (even though we sometimes fail), and bring glory to the Lord Jesus Christ.