Praise be to Allah.
The basis of faith is in the hearts, and so the intention plays a major role in Islamic sharee’ah. This is indicated in the hadeeth which the scholars regard as half of the religion of Islam, and with which many scholars begin their books, such as al-Bukhaari (may Allaah have mercy on him) in his Saheeh. He narrated that ‘Umar ibn al-Khattab said: “I heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say: “Actions are but by intention and each person will have but that which he intended. So whoever migrated for some worldly purpose or for the sake of a woman whom he could marry, his migration was for the purpose that he intended.” (al-Bukhaari, 1). According to the version narrated by Muslim, “So whoever migrated for the sake of Allaah and His Messenger, his migration was for the sake of Allaah and His Messenger, and whoever migrated for some worldly purpose or for the sake of a woman whom he could marry, his migration was for the purpose that he intended.” (Muslim, 2530). Based on the above, this matter may be examined from two angles:
The first has to do with the acceptance of this person’s Islam by Allaah. The hadeeth indicates that it will not be accepted if this (marrying a woman) is the only intention that he has and faith has not entered his heart.
The second has to do with applying the rulings of Islam to him. If this person utters the Shahaadatayn and follows the teachings of Islam, and does not do anything that would nullify his Islam, then he should be treated like any other Muslim, and his marriage to this Muslim woman may be accepted. That is because we are commanded by sharee’ah to deal with people according to how they appear to be; we are not commanded to enquire into what is in their hearts. It says in the hadeeth of Abu Sa’eed al-Khudri that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: I was not commanded to enquire into what is in people’s hearts or to find out their secrets.” (al-Bukhaari, 4004; Muslim, 1763).
Perhaps if this person enters Islam, even if it is with this intention, he will look at the perfection of Islam and be encouraged to form a sincere intention, so he will become sincere towards Allaah and become a good Muslim, and Allaah will accept his Islam. Those who are in touch with this person can advise him to make sure that his intention is primarily to seek the pleasure of Allaah and to enter into Islam truly, and his marriage will then be a consequence or a means of his entering into the blessing of Islam, and not an aim in and of itself. This girl could make marriage to her a means of encouraging him to become Muslim, as happened in the case of Umm Sulaym (may Allaah be pleased with her) and her marriage to Abu Talhah (may Allaah be pleased with him). It was narrated that Anas said: “Abu Talhah married Umm Sulaym, and the dowry between them was Islam. Umm Sulaym had become Muslim before Abu Talhah. He proposed marriage to her and she said, ‘I have become Muslim; if you become Muslim I will marry you.’ So he became Muslim and that was the dowry between them.” (al-Nasaa’i, 3288; classed as saheeh by al-Albaani in Saheeh Sunan al-Nasaa’i, 3133).
With regard to the reason for accepting him – as mentioned in the question – being to increase the number of Muslims, this is not correct, because increasing the number of Muslims, even though this is something good and desirable, is not a reason for accepting anyone who claims to be a Muslim but does not really believe in Islam, because Islam is concerned with quality as well as quantity, it is not concerned only with quantity. One person who sincerely believes in the religion is better than a thousand who are lying about it.