No, not exactly. He is originally an angel, and the angels are indeed spiritual servants/tools by nature being a product of the design of God. Furthermore God assigned Lucifer/serpent to the role he has now. He remains a tool, but it is no longer the case that he is a servant of God – that is incorrect. Nor is he any longer a sole product of the design of God. He is now at least partially a product of human choices and he is the personification of evil. But he is not the origin of evil and he is also a bit of a scapegoat. To be sure God can remove the devil from existence and he plans on doing so, when the role he plays is no longer needed. But to say that he is a servant of God is fundamentally wrong.
In fact 1 Chronicles 21:1 shows the basic absurdity of such a claim. For the suggestion in the text is that the people of Israel are the servants of God. But this is only true in their better dreams and ambitions. The same goes for Christians and all the other religious. They may hope to serve God and God may want them to serve Him, but the reality is that more often than not, they do NOT serve God.
But even this much is not true of Satan. He does not seek to serve God, but rather quite the opposite. The most you can say is that His existence serves the plan of God in a rather indirect manner for the redemption of mankind. His purpose just like the scapegoat is to draw to himself the evil within us and among us, so that in the end all evil may be destroyed along with him.