No one can resist what is termed "the effectual call" of God. Let me explain...
We know from scripture that man is spiritually dead (1 Cor. 2:14; Eph. 2:1). In fact, the Greek word for dead in Eph. 2:1 (nekros) is the same word used for a corpse. A person that is dead is incapable of anything. Since Paul uses the term to describe the spiritual condition of an unbeliever, we can posit that the unbeliever is incapable of anything resembling spiritual life. It takes a unilateral act of God to change that condition. We see that unilateral work of God in Eph. 1:5. While we were still dead in our trespasses and sin "but God". God made us alive while we were spiritually unresponsive. Everything up to this point is the work of God, not the work of man. By the time we get to Romans 10:9-10, the unbeliever has been regenerated. Now we see the believer confessing...freely confessing.
Man does have a choice, but it is a choice with a will that has been newly freed from the bondage of sin. Martin Luther touched on this in his book Bondage of the Will. This analogy will not do the discussion justice, but imagine you were marooned on a deserted island with hardly enough food to keep you alive. You are eventually rescued, but you are emaciated physically. Your cheeks are sunken in, and you ribs easily show through your body. To celebrate your rescue you are served a bountiful meal. Every delicacy you can imagine is put before you. Could you resist partaking of that feast? I seriously doubt it. Multiply that by tens of thousands and we may have a slight understanding of what it would be like for a person to be illumined to the truth (by the Holy Spirit), who understands their pitiful condition, and still rejects the Gospel. To quote the Princess Bride, "Inconceivable!" Once the will of the individual has been set free, there is no greater desire of the will than to accept the free gift of eternal life.
So, does man choose after being illuminated? Yes. Does he choose freely? Yes. Can he choose to reject Christ? No. He cannot reject because the true need of his liberated will has been filled.