All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
This form of marriage is impermissible, because it implies disrespect for the great covenant of marriage, while Allaah The Almighty Says (what means): {And do not take the verses of Allaah in jest.} [Quran 2:231]
However, you should know that if you concluded this marriage contract without the last condition (having no relationship with the woman), it would be a valid marriage with all of its consequences.
That is because marriage is one of the matters in which both seriousness and jest are considered serious. Abu Hurayrah reported that the Prophet, sallallaahu ‘alayhi wa sallam, said: “There are three matters in which seriousness is serious and joking is serious: marriage, divorce, and taking back [one’s wife].” [Abu Daawood, At-Tirmithi and Ibn Maajah]
Scholars said that joking here means intending one thing for another without any relationship between them, and this applies literally to the case in question.
Therefore, we reiterate that it is impermissible for you to do this under any circumstances, and any money paid in return for such marriage is prohibited and ill-gained. Allaah The Exalted Says (what means): {O you who have believed, do not consume one another's wealth unjustly but only [in lawful] business by mutual consent. And do not kill yourselves [or one another]. Indeed, Allaah is to you Ever Merciful.} [Quran 4:29]
If we suppose that the questioner faces a compelling necessity that allows him to commit a prohibition, what about the girl’s father, and under what pretext does he accept to take this money? How will he respond when Allaah The Almighty asks him how he gained this money?
Allaah Knows best.