You certainly must have got a lot of oxygen into your brain with all that jogging**,Gift from God!,**to come up with that question,good for you–I hope that you still looked out where you were going!!;though I should get my brain energized.

-I have two meat pies with sauce in the oven-the health food of my nation!!!
Can I add that not only satan “believes” that Jesus is the Son of God,he also KNOWS it!!We as humans believe something because we put a trust in a statement that we believe is correct ,on the witness or evidence of the person making it;and the person is worthy of belief or trust worthy.In other words we believe that Jesus is the Son of God because what He said and did as is written, in the Scriptures and handed down through the apostolic traditions of our Fathers in the Faith.Hence on Sunday morning we profess our faith in the beliefs as set out in The Apostles Creed.It spells out what we believe as christians,I am assuming that you are a Catholic.But even if you are not ,you still base your beliefs on what the Bible teaches about Jesus and how He proved He was God because of His Ressurection from the dead.
Now as you know Satan ia a fallen ArcAngel,a being who is a spirit(no body) with a high intellect and will.So before his fall he had an infused knowledge of God and then to use his will to adore,love and worship God ,who created angels out of nothing.Yes Satan and other fallen angels rebelled from the sin of pride and were thrust into Hell fire by St.Michael and the other bad angels.
When the Second Person of The Blessed trinity took on human nature and became man,satan (because he had lost his friendship with God) lost his knowledge of God ,so was left in the dark.He knew that a Saviour would come ,as he was there when he tempted Adam and Eve to disobey God,He also knew of the promise that Gods’Chosen People were to be restored by a Messiah or Savior.So after the birth of Jesus,satan wispered into Herods’ear to kill every first born male(females get all the breaks) in the hope that this would thwart God’s plan,Satan knew something was brewing-perhaps it was another prophet for all he knew.You know scripture,so there was the tempation in the desert,how Jesus lived a hidden life and satan could not forment people to kill Jesus.Even Our Lady or Mary the Mother of Jesus brought forward her Sons’ public life-for His first answer was that His time had not come.You know the ending ,at least satan thought that it was,as he was able to lead others to kill Jesus.So in one sense, satan was formulating his" belief"about who Jesus was,but could you imagine his hatred,anger,malicious hurt pride when Jesus rose from the dead.Satan not longer was in darkness,he knew then that Jesus was The Son of God ; but his kingdom on this earth was taken back from under him.That is why since he cannot get at God any more ,he can and does attack the people who call themselves Christians and believe that Jesus is Lord!! ( But only if we are not baptised or believe in The Gospel or give into serious sin and hardening our hearts by not repenting—for Catholics—confession,The Bead of Life in receiving The Eucharist—prayer and penance etc.)
So no satan is not even technically a Christian even in the sense that you put in your thread.
St.Michael,defend us from the powers of satan,help us to believe that Jesus is The Son of God and to act out this creed with our actions.Amen.
p.s.I only used small s for satan-as a capital one shows a sign of respect or importance.I only use he for satan in the general english language as he is all evil spirit.