The best place to find the answer to that question was in the Bible. The answer is no. Everyday believers desire to sin. When that happens, who is to blame? Usually ?Satan made me do it? is the typical excuse.

Wrong! Our desire to sin comes from our lusts (James 1:13,14), the flesh (Galatians 5:19-21) and evil hearts (Mark 7:21,22). Satan knows these weaknesses and uses them to his advantage. If Satan cannot cause us to sin, he certainly cannot indwell in us. When we are told to put on the whole armour of God, it is meant to protect us from the outside evils not from evil that is ?possessing? us (Ephesians 6:13).
There are many places in the Bible that clearly show how impossible it is to be a believer and be demon possessed.

First, in I Corinthians 6:19 it states that ?your body is the temple of the Holy Ghost which is in you...? Something holy and something evil cannot indwell the same person at one time and once you are a believer, the Holy Spirit is indwelling in you at all times even during those times in your life when you may not be filled with the Spirit. Another verse that I find to be helpful in this issue is I John 4:4, ? Ye are of God, little children, and have overcome them: because greater is he that is in you, than he that is in the world.? Christ is in us and Satan is in the world so I would have to say we are Christ possessed.

Satan uses this idea people have that we can be possessed to his advantage I think and people start looking to the wrong places for comfort and salvation. All along we need to look inward to focus on Christ and not on the world.Finally, the last scripture reference I would like to use is Romans 8:38-39, ? For I am persuaded, that neither death, nor life, nor angels, nor principalities, nor powers, nor things present, nor things to come, nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord.? To say that a believer can be possessed by Satan is to say that we are separate from God and present with Satan. God assures me through the Bible that that will never happen.

Amen!
Bibliography:
Bible is the only source