If you mean by "Satan" you mean a spiritual being named "Satan," then No. The word from the Hebrew is "ha satan" and simple means an adversary and can apply to anyone who stands against God, or someone else. However, Paul was specifically calling out "the god of this age."
in whom the god of this age did blind the minds of the unbelieving, that there doth not shine forth to them the enlightening of the good news of the glory of the Christ, who is the image of God; (YLT)
The KJV incorrectly used the word "world." The correct word is "aionos" or age. (1) The book was written about 55-56 AD (2) during the reign of Caesar Nero who called himself a god, or the son of a god. They were living under the Roman emperor cult worship of pagan gods. Paul was referring to a living man of that day and time who was deceiving the people, and whom our Father in heaven had already marked for judgment.
The subject matter of 2 Cor. 4 was speaking of deception.
but did renounce for ourselves the hidden things of shame, not walking in craftiness, nor deceitfully using the word of God, but by the manifestation of the truth recommending ourselves unto every conscience of men, before God; (YLT)
Paul told them that he and the other apostles / disciples were not distorting the truth of God's word, but speaking the truth of Yeshua's sacrifice and the gospel of Christ. This implies that others were not speaking truth. Paul spoke of the tribulation (vs. 8, 9) and persecution they were experiencing.
So, the date of this book puts that persecution and tribulation before the time that Nero blamed the Christians for the burning of Rome, before 64 AD. Therefor, this persecution was from the Sanhedrin, scribes and Pharisees out of Jerusalem.
The "god of this age", that age still being the age they were living in during the 1st century AD, before the destruction of the temple in Jerusalem (AD 70), were those rulers in Jerusalem that were still living under the Mosaic law and the temple sacrifices. These rulers were sending out Judaisers to pull people back under the law preaching circumcision and observance of feast days, and other Mosaic temple laws.
That adversary (satan) was a living man who opposed God by rejecting the promised Messiah, Yeshua. Candidates for this role include King Agrippa, Annanias, his son Jonathan, and other rulers of the Sanhedrin council who all were under the rule of Caesar Nero at that time. (3)
The way that adversary (god of this age) blinded the people was through the pressure of tribulation - obey us or else - and persecution to force them to turn back under the Mosaic law. They lied and conspired to deceive by twisting the scriptures. The same way many people have been deceiving millions today to believe other than what the scriptures say. (4)
Dating The New Testament
Who was High Priest in 56AD
What Does The Bible Really Say....