Well, yes, they do sin obviously.  A Christian can fall into sin, but he won't stay there.  God will always pull him lovingly back into fellowship with Him.  Perhaps the better question is:  Can a Christian live in a lifestyle of constant sin?  1 John 1:6 says:

If we say that we have fellowship with him and walk in the darkness, we lie, and don't tell the truth.  

Your comments welcome!