The answer to this question is "Yes!"
The Bible is clear: human beings are not puppets on God's hand. We are not machines programmed by God to act out a script. God created humanity in his image, and part of that image is to be reasoning, self-activated beings. When God talks with one of His children in the pages of the Bible, God is not talking to a flesh-veiled version of Himself! When God in the Bible blames someone for sinning, it is because they knew what was right and chose to do otherwise.
Consider the example of Eve in Genesis 3. Eve did not sin because of having a sin-nature. Eve was still innocent and undefiled. Eve was created with a righteous nature, yet she chose to sin (which proves, by the way, that choices are not caused by one's nature). How did Satan lead her into sin?
First, he planted into her mind doubt toward the Word of God. Second, he deceived her into believing that nothing bad would happen as a result of sinning. That is all Satan had to do, and that is what Satan does today.
Eve's error regarding the Word of God probably undermined her belief that she would die, because she misquoted the Lord (the Lord never said that she would die if she touched the tree). So, when she touched the tree and she didn't die, she would have disbelieved the rest of God's warning. But she was wrong in her quotation of the Lord's warning in the first place.
Eve's motive for sinning was the desire for a perceived benefit. This is part of the natural image of God in man. Human beings have never lost this motive. From the youngest baby, to the oldest criminal, to the most serious saint, everyone is motivated by benefit. God Himself does everything he does out of benefit -- i.e., He does everything H does because it brings Him pleasure. This natural attribute of God is duplicated in human beings, and falling from grace did not extinguish it. Eve evaluated the fruit from a purely pragmatic perspective. It was pretty, it was nutritious, and it could make her wise.
Human beings have been making choices on the basis of benefit (or, negatively stated, the avoidance of loss) ever since. What changed when Adam sinned? For one thing, man's mind is full of foolishness, and deceived by the devil. People keep on seeking benefit, but what they think will benefit them is wrong. Solomon says there is a way that seems right to a person, but the end thereof is death.
Second, humanity's natural desires are unbalanced and intemperate. The human desires for safety, respect, sexual pleasure, accomplishment, justice -- these were all originally created by God, and also reflect the natural image of God in man. But in the absence of the Holy Spirit, these natural desires run riot, like a powerful horse running without bit or bridle.
A person's choices are controlled by what the person believes to be true. If the person is deceived by the devil, then their will is still free, but they are choosing in wrong directions. When the Lord brings the light of the Word of God into someone's life, however, and the Spirit of God uses His word to enlighten the heart, then accountability settles upon. People see God's existence in nature, but choose not to honor Him, because they are foolish. As a result, God manifests His wrath upon the wicked world (Romans 1:18ff).
But people can also respond to the light of God's Word. Cornelius the centurion was a Roman soldier who, nevertheless, must have been exposed to God's word. The Bible enlightened Cornelius' mind. Luke calls Cornelius "devout", and the Lord accepted his prayers and alms even though Cornelius was an unregenerate man (Acts 10).
The light of the Word of God will create a turning-point moment in everyone's life, where we pass from ignorance into knowledge. It is at that point that we must choose how we will proceed. God is merciful to the ignorant, but stern toward willful sin. He does not cause our choices to sin, and He does not force us to believe.