Let me first answer that with a resounding "YES" with one small caveat; it is perfectly acceptable to come to the Lord in a messy state, but you have to go with a willingness to want to change it. If truth be told, most of us came that exact way, maybe a different circumstance or situation but in essence the same. To speak plainly, God will accept you in the state right where you are, but he cannot use you if left in that state. Don't worry; I hope to make this much clearer in the subsequent paragraphs.
The Bible in Romans 3:23 says: "For all have sinned and come short of the Glory of God"; in other words, no man, woman, or child past or present is without Sin. I do not say this to diminish the consequence of Sin but rather to show that everyone has fallen short of God's standards or glory. This is very important to understand because people put degrees on Sin, but the Lord does not. Some believe that having an affair is a 1st-degree sin offense, but if you lie, that is a 3rd-degree offense; if you harm someone, that is a 1st-degree sin offense, but if you steal, that is a 2nd-degree offense. It is true, the ramifications of those acts established by the law of the land come with different degrees of consequence or punishment, but God sees all these acts as falling short of His Glory. It is evident in Romans 3:23 that God did not distinguish between the types of Sin but said all had done it regardless of the kind of Sin.
Knowing these facts should answer the question of whether or not God can still use you? "Sure He Can," but not in a sinful state. Now let's talk about how He prepares those He wants to use or that have a desire to be used by God. First, let's take a look at the disciples of Jesus. All were men so clearly not without Sin as established by Romans 3:23. How about the Samaritan women at the well-articulated in St. John 4:1-25, where she had five husbands, and the man she was currently with was still not her husband. What about Saul before he became Paul, who wrote many books of the new testament, he was persecuting Christians even to death. All of these impactful individuals of the Bible who God used were not without Sin, and one could even say their lives were quite messy. So what happened? Each of them had an encounter with Jesus, and the encounter changed them, sending them down a different path, a different direction, with a different purpose. The Good News is, it can happen to you as well.
Today, an encounter with Jesus is much different than the happenstances of the past. You can prompt an encounter with Jesus right now, right where you are, by merely calling out to Jesus and saying, Lord, "I am a Mess, but I want to be changed." The Lord loves honesty because He is the truth, but more importantly, He loves humility and a broken spirit that wants to be repaired and restored. Don't let anyone get in your way today from an encounter with Jesus; your life depends on it, and he wants to give you a life full of abundance and peace. You may be a mess today, but Jesus can change you in the twinkle of an eye, making your tomorrow much brighter.