Yes. But his long tenure there is already over! He is out for a short while now to deceive the people of the world and if possible, even the believers.

And I saw an angel come down from heaven, having the key of the bottomless pit and a great chain in his hand. And he laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him a thousand years, and cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more, till the thousand years should be fulfilled: and after that he must be loosed a little season. Rev 20:1-3. Bottomless pit (Paadhalam in Thamizh) is the place where all dead go!

The key (power / right / authority) of the bottomless pit was given to a star that fell from Heaven unto the earth – Rev 9:1; Rev 12:9. This star Satan retained his power / right / authority over death and all dead mankind until Jesus descended to this place (after His death on the cross) – Rom 10:7 to lead the captives (to death) captive when ascending up on high – Eph 4:8. The souls of the believing dead went with Him to heaven (on high). This was possible because, through death He destroyed him that had the power of death, that is, the devil – Heb 2:14. That is why He could authoritatively say: “I am He that lives and was dead; and, behold, I am alive for evermore, Amen; and have the keys of hell and of death”. – Rev 1:18. This key is the one the angel (one of those servants who run at God’s bidding) that came down from heaven had. He cast Satan into the bottomless pit, bound him with a chain and locked him in at the time when the Church was established on the day of Pentecost.

Until the death and resurrection of the Lord Jesus Christ, the believing generation was only Jewish while the nations of the earth were pagans and idol worshippers completely sold out to Satan and his deception. Tamar, Rahab and Ruth were women and exceptions! Only after the Church was established on earth did God reveal the mystery to Apostle Paul (and also to Peter at the house of Cornelius) that the gentiles were also an integral part of His church. Thenceforth, Satan could not continue deceiving the non-Jews (the nations). Local churches were established in various cities beginning from Jerusalem to Judea to Samaria and to the end of the earth. Nations were saved by the grace of God and the Gospel of the Lord Jesus Christ. This preaching of the gospel and the saving of the nations would happen for a long time – a thousand years is a long time – it is not 360,000 (Jewish) / 365,250 (secular) days.