Was Paul's Relationship with Jewish Leadership Close Enough to Act as Their Agent?

At the end of Acts 7 you had Saul approve of the stoning of Stephen

At this they covered their ears and, yelling at the top of their voices, they all rushed at him, dragged him out of the city and began to stone him. Meanwhile, the witnesses laid their coats at the feet of a young man named Saul. While they were stoning him, Stephen prayed, “Lord Jesus, receive my spirit.” Then he fell on his knees and cried out, “Lord, do not hold this sin against them.” When he had said this, he fell asleep. Acts 7:57‭-‬60 NIV http://bible.com/111/act.7.57-60.NIV

and then the open of chapter 8 says that a great persecution began

And Saul approved of their killing him. On that day a great persecution broke out against the church in Jerusalem, and all except the apostles were scattered throughout Judea and Samaria. Godly men buried Stephen and mourned deeply for him. But Saul began to destroy the church. Going from house to house, he dragged off both men and women and put them in prison. Acts 8:1‭-‬3 NIV http://bible.com/111/act.8.1-3.NIV

At the open of chapter 9 Saul was "still breathing murderous threats" against the Christians

Meanwhile, Saul was still breathing out murderous threats against the Lordʼs disciples. He went to the high priest and asked him for letters to the synagogues in Damascus, so that if he found any there who belonged to the Way, whether men or women, he might take them as prisoners to Jerusalem. Acts 9:1‭-‬2 NIV http://bible.com/111/act.9.1-2.NIV

While it usually just states that those he persecuted were arrested, remember that being arrested in those days didn't mean 3 hots and a cot, it was hard labor and regular beatings and often death in prison as Paul mentions in Acts 22

I persecuted the followers of this Way to their death, arresting both men and women and throwing them into prison, as the high priest and all the Council can themselves testify. I even obtained letters from them to their associates in Damascus, and went there to bring these people as prisoners to Jerusalem to be punished. Acts 22:4‭-‬5 NIV http://bible.com/111/act.22.4-5.NIV

In 1 Tim 1:15 he calls himself the very worst of sinners

Here is a trustworthy saying that deserves full acceptance: Christ Jesus came into the world to save sinners—of whom I am the worst. But for that very reason I was shown mercy so that in me, the worst of sinners, Christ Jesus might display his immense patience as an example for those who would believe in him and receive eternal life. 1 Timothy 1:15‭-‬16 NIV http://bible.com/111/1ti.1.15-16.NIV

Even if you say at the very least, that he was merely a policeman, arresting Christians and sending them to jail, he would need the authority to do that and that would come from the Jewish leaders.

I would also say that Paul was very well known by the Jewish leaders to have been granted authority. 1st, the fact that prior to him making the request from the leaders to be given authority to persecute the church, we already had the authority to approve of Stephen's stoning. 2nd, Luke mentions Saul's pedigree in Acts

But a Pharisee named Gamaliel, a teacher of the law, who was honored by all the people, stood up in the Sanhedrin and ordered that the men be put outside for a little while. Acts 5:34 NIV http://bible.com/111/act.5.34.NIV

When they heard him speak to them in Aramaic, they became very quiet. Then Paul said: “I am a Jew, born in Tarsus of Cilicia, but brought up in this city. I studied under Gamaliel and was thoroughly trained in the law of our ancestors. I was just as zealous for God as any of you are today. Acts 22:2‭-‬3 NIV http://bible.com/111/act.22.2-3.NIV

and Paul mentions his pedigree again in Galatians 1 to give plenty of how he could have been trusted with such a task

For you have heard of my previous way of life in Judaism, how intensely I persecuted the church of God and tried to destroy it. I was advancing in Judaism beyond many of my own age among my people and was extremely zealous for the traditions of my fathers. Galatians 1:13‭-‬14 NIV http://bible.com/111/gal.1.13-14.NIV

Now the the point that Paul could have been sent to modify the early church, if you were trying to infiltrate and modify the early church, the last thing you would do is send the guy who persecuted the early church the most. You could have taken no-name Pharisees and send them. Paul was the most zealot of them all and it took him years to gain the trust of the disciples. Also, the majority of the Christians were previously Jews. Given that even the Pharisees would not let the Roman soldiers mess with the disciples because they were still considered Jews, they would have pursued bring the "followers of the Way" into alignment as a sect of Judaism but Paul took it the opposite way.

When false teachers began to take churches back to Jewish practices like in Galatians 1, he turned them back to the Gospel and away from Judaism

I am astonished that you are so quickly deserting the one who called you to live in the grace of Christ and are turning to a different gospel— which is really no gospel at all. Evidently some people are throwing you into confusion and are trying to pervert the gospel of Christ. Galatians 1:6‭-‬7 NIV http://bible.com/111/gal.1.6-7.NIV

He mentions similar things at other churches but if he was sent to modify the church, he was terrible at it.