Certainly, provided their heart is receptive and the Holy Spirit permits it. Don't sell the Lord short there. You would be smug to think that the Lord could not accomplish this.
Oh I agree 100% However the key phrase is "provided their heart is receptive." Why would some have hearts that are not receptive? Well here's one example. Have you read the Islamic description of hell? In their conception of hell demons tear the skin off your body. It grows back and the demons tear it off again. This goes on for all eternity and each time the skin is peeled off, you suffer more. Islam teaches that to turn away from Islam means you will go to hell. So the prospect of this horrible, horrible punishment might keep a person's heart from being receptive. Some people are very impressionable. And such a person who has had this fear ingrained in them, is sort of brainwashed. Part of their free will has been tampered with and so their hearts are not receptive. And it's not really their fault.
I do not think we can say for certain that God automatically comes in a fixes this disturbed pattern and makes the person receptive to grace. I think he does it sometimes and sometimes not. Sometimes children die before they are old enough to understand the gospel and accept it. God lets that happen and we don't know why but we believe he is merciful and does not send that child to hell.