The marriage of the adulterer to the women with whom he committed illegal sexual intercourse is not considered an atonement. The atonement for adultery is only in two things: Either the punishment is imposed upon him if news of it reaches the authorities, or he must turn in repentance to Allaah, the Almighty, the All-Powerful due to this act of adultery, improve his behaviour and stay away from places of temptation and fornication.
As for him marrying this women, it is forbidden for him to marry her, and it is forbidden for her to marry him, because Allaah says:
الزَّانِي لَا يَنكِحُ إلَّا زَانِيَةً أَوْ مُشْرِكَةً وَالزَّانِيَةُ لَا يَنكِحُهَا إِلَّا زَانٍ أَوْ مُشْرِكٌ وَحُرِّمَ ذَلِكَ عَلَى الْمُؤْمِنِينَ
"The adulterer-fornicator marries not but an adulteress-fornicatress or a Mushrikah; and the adulteress-fornicatress, none marries her except an adulterer-fornicator or a Mushrik [and that means the man who agrees to marry (have a sexual relation with) a Mushrikah (female polytheist, pagan or idolatress) or a prostitute, then surely, he is either an adulterer-fornicator or a Mushrik (polytheist, pagan or idolater). And the women who agrees to marry (have a sexual relation with) a Mushrik (polytheist, pagan or idolater) or an adulterer-fornicator, then she ie either a prostitute or a Mushrikah (female polytheist, pagan or idolatress)]. Such a thing is forbidden to the believers (of Islamic Monotheism)" [An-Nur 24:3]
Unless they repent to Allaah with sincere repentance and regret what has happened and improve their behaviour. Then there is no objection to him marring her, just as any other may marry her.
As for a child that may result from illegal sexual intercourse, he is not considered the son of his father, according to the generality of the words of the Messenger (sallAllaahu `alayhi wa sallam):
الولد للفراش وللعاهر الحجر
"The child is attributed to the mattress on which he was born and Al-'Ahir is to be stoned." (Al-Bukhari no. 6818 and Muslim no. 1458)
Al-'Ahir means the one who commits illegal sexual intercourse. That is, he has no child, that is the meaning of the hadeeth. Even if he married her after repenting, the child created from the first water (i.e. the sperm of illegal sexual intercourse), even though he claims him as his son, because he is not a legitimate son.