Nobody, in my opinion, who made true commitment to follow Jesus and walked with Him for some time, is capable of staying in habitual sin.
Do you still sin? If you sin once a week, or once a day, or one a year, is it not a habit? This "cannot habitually sin" doctrine is a lie. You sin everyday, and if that is not practicing sin, I don't know what is.
You are not saved by making a committment to follow Jesus. You are saved by accepting His righteousness by grace through faith. You see, making a commitment to follow Jesus is a work that man tries to do. God's free grace requires no work, but for you to believe that what He has said is true.
When you are saved, you are made the righteousness of God in Christ. If you sin, you sin as a saint, and like the verse you posted says - if any man sin, we have an advocate with the Father, Jesus Christ the Righteous. (1 John 2:1-2)
So to answer your question, yes, a homosexual can be saved - however, they will not be saved unless they first recognize that they are sinners, just like everyone else (this is repentance), and then come to Christ. Will they change? Yes, but it may not be immediate, and it may take a long time for them to fail over and over again before they come to a place where they see they have no strength and must rely on God's strength.