Praise be to Allah.
It is haraam for a man to have intercourse with his wife once he has entered ihram for Hajj or ‘umrah; it is also haraam for her to obey him in that regard or entice him to do that.
In the answer to question no. 119134 we have explained the ruling concerning that.
If he has intercourse with her before entering ihram for ‘umrah or after completing it, there is no blame on him or on her, even if that happened in Makkah, and even if they were intending to enter ihram again for ‘umrah or Hajj, after exiting ihram and having intercourse, because what is prohibited is having intercourse after entering ihram for either ritual, or before exiting ihram. But if it is before entering ihram or after completing the ritual, that is not prohibited.
The scholars of the Standing Committee said:
If a man has intercourse with his wife during the period in which he exited ihram between ‘umrah and Hajj – i.e., he had completed the actions of ‘umrah and had not yet entered ihram for Hajj – then there is no blame on him.
End quote from Fataawa al-Lajnah ad-Daa’imah (11/187)
There is no blame on a man for having intercourse with his wife with the aim of satisfying his desire, if he intends thereby to keep himself and his wife chaste, and he will be rewarded for that.
If he combines with that the hope of having righteous offspring, then this will bring an even greater reward, whether that happens before entering ihram for Hajj or ‘umrah, or after completing the rituals, or at any other time, so long as there is no shar‘i impediment.
Abu Dawood (2050) narrated from Ma‘qil ibn Yasaar that the Prophet (blessings and peace of Allah be upon him) said: “Marry women who are loving and fertile, for I will boast of your numbers before the other nations.”
Classed as saheeh by al-Albaani in Saheeh Abi Dawood.
Ibn ‘Uthaymeen (may Allah have mercy on him) said:
The Muslims should have as many children as they can, so as to fulfil the wish of the Messenger (blessings and peace of Allah be upon him) and so that the Muslim ummah may be self-sufficient and have no need of others, and so that they will be respected by others. The more the ummah increases in numbers, the more status it will have before its enemies and the more self-sufficient it will be.
End quote from Fataawa Noor ‘ala ad-Darb (21/2)
However we should point out that the virtue of such actions has nothing to do with travelling for Hajj or ‘umrah; rather whatever is permissible is permissible regardless of whether it is done during one’s journey or in one’s own country, and whatever is recommended is likewise. There is no particular virtue in doing that during a journey for Hajj or ‘umrah.
And Allah knows best.