Yes. After the son is a son he can give his heart to his father. And after we are sons of God we can give our hearts to God. In fact, such is the result of our sonship and not the cause of it.
So then Esau was accepted by God for he is the Son of Isaac, and Ishmael was accepted by God for he was the son of Abraham. They were sons and called sons. This Parable and these references to the elder son, as backed up by Calvin and Henry, clearly show that Christ was showing the Pharisees and scribes as the elder son, going by what you have stated that they are called sons and therefore are believers and so by your belief is that all that are called sons are therefore saved would carry over to the Pharisees and scribes as they are seen in the elder son.
Yet it is clear from the text and the meaning Jesus drew from it that the elder son clearly was not saved by the actions he showed. The Prodigal was wayward in sin who is like the publican and sinners received by the Lord. Why because they came to Him in belief that He would save them. We see who the Parable was directed to in Luke 15:
2 And the Pharisees and scribes murmured, saying, This man receiveth sinners, and eateth with them.
3 And he spake this parable unto them, saying,
He spake this parable to the Pharisees and scribes. Clearly an object lesson for them. They are seen in the Elder son, they have been in their minds been faithful to God. They haven't been rewarded as these publicans and sinners have. They have been faithful, followed the rules, offered sacrifices, write scripture and are faithful. They expect there works to save them and that point was driven home when Christ said the father of these prodigals stated "
thou art always with me" and they felt that was them. Now we see:
Romans 8:14 For as many as are led by the Spirit of God, they are the sons of God. Was the elder led by the spirit to be as he was? The elder had been with the father and faithfully worked for his approval all his life, he was his fathers son. Israel had been a called out nation the Pharisees and scribes were sons of Abraham and had always been SONS of Abraham, did that make them saved? They were in their minds "
always with" God always belonged to God and yet were they actually sons?
The Prodigal represented, the Publicans, harlots and sinners that Christ accepted, for we see Luke 15:
"1 Then drew near unto him all the publicans and sinners for to hear him.
2 And the Pharisees and scribes murmured, saying, This man receiveth sinners, and eateth with them."
This was the reason for the Parable. The ones murmuring about the sinners being received and even having a meal with them were not saved. So too the Elder sons is the type or mirror of them, therefore unsaved by the meaning of the story. Just as the 99 sheep were lost how do we know because they were left in the Wilderness, not in the sheepfold. Then we see this right before Christ speaks the parable of the son,
Luke 15:
10 Likewise, I say unto you, there is joy in the presence of the angels of God over one sinner that repenteth.
The prodigal is the sinner that repented, is it by works no way. He came to himself we are to he realized Himself a sinner came to Christ. Very Clear how salvation works, realize you are a sinner and that God the Father formed the plan and Jesus became the sacrifice for your sin and Call upon Him for Salvation, the Holy Spirit revealing it to all through His convicting them. All God's work none mans.
Romans 14:
8 For whether we live, we live unto the Lord; and whether we die, we die unto the Lord: whether we live therefore, or die, we are the Lord's.
9 For to this end Christ both died, and rose, and revived, that he might be Lord both of the dead and living.
Whether saved or lost we are the Lord's, every human ever born has belonged to Him, for He died and rose and revived to be the Lord of the living (saved) and the dead (lost). We all belong to the Lord.