Will God allow Satan to have any souls of man? I was once heard that God would not let Satan gather any souls of man.
Nowhere does the Bible talk about Satan "gathering" souls of men. In a very real sense he doesn't need to gather souls, because we give them to him without effort on his part. From the first time we sin we are his without him having to gather us.
Can Satan have our souls? Peter says he "as a roaring lion, walks about, seeking whom he may devour." (1 Peter 5:8) Peter should know. Jesus told him, "Satan hath desired to have you, that he may sift you as wheat." (Luke 22:31) So it would seem that Satan can certainly have us, if we let him. That is the thing about it, though; we must let him have us. If we resist him, he is powerless. "Submit yourselves therefore to God. Resist the devil, and he will flee from you. Draw nigh to God, and he will draw nigh to you." (James 4:7-8)
As I wrote before, as soon as we sin we are Satan's. Without forgiveness of our sins we will remain his. That is where submission to Christ through immersion (baptism) comes in. Until such time as we receive forgiveness of sins through that means, we remain Satan's. Once we become Christ's, we are no longer Satan's slaves.
Whoever says God will not let Satan have the souls of man has clearly not read the Bible. The good news of the Bible is that we don't have to let Satan win.