No, the Sanhedrin at the time of Christ apparently had lost the power to execute the death penalty.
In one important matter, however, the authority of the Sanhedrim was abridged: the Romans deprived it of the power of life and death. They might pronounce sentence of death, but the sanction of the Roman governor had to be obtained before that sentence could be carried into execution. According to the Talmud, the Sanhedrim was deprived of the power of inflicting capital punishment forty years before the destruction of Jerusalem; whereas formerly it alone of all the Jewish courts possessed this power (Joseph. Ant. xiv. 9. 3). Hence the remark of the Jewish rulers to Pilate: “It is not lawful for us to put any man to death” (John 18:31). The stoning of Stephen is not an exception to this; for that happened during a popular tumult, and when, in all probability, there was a vacancy in the Roman procuratorship, after Pilate had been sent to Rome. A similar instance occurred after afterwards, when James the Just was put to death by the high priest Ananus during the absence of the Roman governor: for Josephus expressly informs us that this was an illegal assumption of power, and for which Ananus was deposed from the high-priesthood (Ant. xx. 9. 1). (A CRITICAL AND EXEGETICAL COMMENTARY on the ACTS OF THE APOSTLES by PATON J. GLOAG, P153)
This is directly proven from the works of Josephus under the section " CHAPTER 9
CONCERNING ALBINUS UNDER WHOSE PROCURATORSHIP JAMES WAS SLAIN; AS ALSO WHAT EDIFICES WERE BUILT BY AGRIPPA"
but this younger Ananus, who, as we have told you already, took the high priesthood, was a bold man in his temper, and very insolent; he was also of the sect of the Sadducees, who are very rigid in judging offenders, above all the rest of the Jews, as we have already observed; (200) when, therefore, Ananus was of this disposition, he thought he had now a proper opportunity [to exercise his authority]. Festus was now dead, and Albinus was but upon the road; so he assembled the sanhedrin of judges, and brought before them the brother of Jesus, who was called Christ, whose name was James, and some others, [or, some of his companions]; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned; (201) but as for those who seemed the most equitable of the citizens, and such as were the most uneasy at the breach of the laws, they disliked what was done; they also sent to the king [Agrippa], desiring him to send to Ananus that he should act so no more, for that what he had already done was not to be justified; (202) nay, some of them went also to meet Albinus, as he was upon his journey from Alexandria, and informed him that it was not lawful for Ananus to assemble a sanhedrin without his consent; —(203) whereupon Albinus complied with what they said, and wrote in anger to Ananus, and threatened that he would bring him to punishment for what he had done; on which king Agrippa took the high priesthood from him
As the high Priest was removed from his position for assuming the power to execute James the brother of Jesus, without the higher permission of the Roman government via Agrippa (according to the Jewish historian Josephus in those days) it is very difficult to reasonably maintain an alternative theory.