No, Satan is a fallen angel who was, before he was a fallen angel, a righteous servant of God. Just as are all of the god-honoring angels. But Satan found sin in his heart and tested God to rebel against His ultimate authority and God set him in his place until his destruction which has been established. Being a servant of God would imply that he will do what God wants. I'm pretty sure that Satan isn't doing what God wants. I mean, how fair would that be if God intentionally set Satan upon us. If we would have remained sinless and Satan would have never visited the earth, then we'd still be living in paradise. You think God told him to do that?
That would just seem to be cruel of someone to take people who would have been good and then set them the test that if they failed they would then live a life of strife and struggle and need and pain and suffering. No, I don't think God sent Satan to mankind as some sort of test that they failed. Satan came here all on his own against God's will. He spoke with the new creature that God had created and convinced her withing minutes to defy God. Satan is not God's servant. Although, if you want to consider him like Nebudchudnezzer, a sword of the Lord, I suppose one might make that stretch. But Israel had done evil before God sent Nebbie to overrun their cities for their defiance. Eve had done no evil before Satan spoke with her.