Can they get married and agree not to be intimate until their financial situation improves?

Marriage is one of the means of obtaining provision, as
Allaah says (interpretation of the meaning): 

“And marry those among you who are single (i.e. a man who
has no wife and the woman who has no husband) and (also marry) the Saalihoon
(pious, fit and capable ones) of your (male) slaves and maid‑servants
(female slaves). If they be poor, Allaah will enrich them out of His Bounty.
And Allaah is All‑Sufficient for His creatures’ needs, All‑Knowing (about
the state of the people)”

[al-Noor 24:32]

al-Qurtubi (may Allaah have mercy on him) said: “those
among you who are single” refers to those who have no spouse, men and
women. 

And he said: “If they be poor, Allaah will enrich them out
of His Bounty” means: do not refrain from getting married because the
man or the woman is poor. If they are poor, Allaah will make them
independent of means by His bounty. This is a promise of independence of
means to those who get married, seeking the pleasure of Allaah and seeking
to protect themselves from sin. Ibn Mas’ood said: Seek independence of means
through marriage, and he recited this verse. ‘Umar (may Allaah be pleased
with him) said: I am surprised by those who do not seek independence of
means through marriage, when Allaah has said, “If they be poor, Allaah
will enrich them out of His Bounty.” Something similar was also narrated
from Ibn ‘Abbaas (may Allaah be pleased with him). 

Al-Qurtubi also said: This verse indicates that the poor man
should get married, and he should not say, How can I get married when I have
no wealth? For his provision comes from Allaah. The Prophet (peace and
blessings of Allaah be upon him) gave in marriage a woman who came to offer
herself to him, to a man who hadnothing but a single izaar (waist-wrapper).
End quote from Tafseer al-Qurtubi (12/218). 

And he (peace and blessings of Allaah be upon him) said:
“There are three who are all entitled to Allaah’s help: the one who fights
for the sake of Allaah; the mukaatab who wants to pay (the price of his
freedom); and the one who gets married seeking chastity.” Narrated by
al-Tirmidhi (1579), al-Nasaa’i (3166) and Ibn Maajah (2509). This hadeeth
was classed as hasan by al-Albaani in Saheeh al-Tirmidhi. 

If this young man is going to do the marriage contract, and
his wife is going to stay in her father’s house until they can afford to set
up home together, there is nothing wrong with that. But he has to look for
work so that he can spend on himself, his wife and his house, so that his
wife and her family will not be adversely affected if it takes too long. 

If what is meant is that his wife will move to his house but
they have agreed not to be intimate, so that they will not have children at
this stage, that is not appropriate for several reasons: 

1-Refraining from intimacy means
missing out on something that is one of the most important aims of marriage,
which is having children.

2-Refraining from having children
for fear of poverty is contrary to putting one’s trust in Allaah, and it is
an imitation of the people of Jaahiliyyah who used to kill their children
for fear of poverty. Allaah has guaranteed to give provision for every soul,
as He says (interpretation of the meaning):

“And no moving (living) creature is there on earth but its
provision is due from Allaah. And He knows its dwelling place and its
deposit (in the uterus or grave). All is in a Clear Book (Al‑Lauh Al‑Mahfûz
— the Book of Decrees with Allaah)”

[Hood 11:6] 

“And in the heaven is your provision, and that which you
are promised”

[al-Dhaariyaat 51:22]

But we must point out two things: 

1 – With regard to marriage, it is essential that the
conditions be fulfilled, which is the consent of both parties and that there
be no legal impediments such as their being mahrams (relatives to whom
marriage is forbidden) or their being related through breastfeeding. The
woman’s wali (guardian) and two witnesses must also be present, otherwise
the marriage is not valid. 

2 – It is not permissible for a man and woman to form a
relationship before marriage, because of the many negative consequences to
which that will lead, such as falling in love, sickness of the heart
(because of sin), looking at one another, being alone together, speaking
softly to one another and other things that Allaah has forbidden. 

And Allaah knows best.