I’ll step into the minefield and give my $.02 on this matter.
I’m not sure I can answer the title question, but here are my thoughts.
There are several intertwined concerns in this scenario.
It seems to me that if the girl in question is a minor, punishment for bad behavior or sin is primarily her parents’ concern (and responsibility- same goes for the punishment of the boy in question) and is not the concern of the school unless the bad behavior/sin took place on school grounds, caused the school to be source of scandal in the community, or put the school at risk of scandalizing its other students.
It is generally not within the purview of a school to punish sin or bad behavior in students except if it takes place during the time the school is specifically responsible for the student (or when the student is specifically associated with the school.) (Thus teachers don’t give students detention for disrespecting their parents or treating their siblings or friends badly, etc.)
I’d conclude punishment for the sin of premarital sex is not the school’s concern, but the parents’ (of both students) responsibility.
In dealing with the pregnant student, it seems to me that the school would want to avoid giving scandal in two ways:
First, a Catholic school cannot appear either in the community, or to its student body, as condoning premarital sex.
Certainly not all female students who have premarital sex become pregnant, and boys do not visibly carry evidence of their sin as girls must, but the fact of the matter is that this poor girl’s sin (and the boy who fathered the child) is now public and so must be addressed. The school cannot do nothing in this situation.
Secondly, however, in the present secular culture of death, a Catholic school must avoid spreading the false notion that pregnancy itself is what should be avoided (not premarital sex) and it must not provide further temptation to students who may be committing the same sin of premarital sex as the girl and boy in question, to committ the (much worse, I think) sin of abortion. The school must also (as far as it can without giving scandal otherwise) avoid indirectly promoting contraception, as well.
The school has an obligation to uphold the Church’s teaching that every human life has dignity and value, regardless of how it was conceived.
So, I think, if the school punishes the unwed female student by expelling her and does not punish the father of the child (even if it’s because he hasn’t been identified), it risks communicating to the student body that a) pregnancy in the punishable offence and b) that only girls are accountable in this situation (which perceived injustice may become an obstacle to other students’ faith.)
On the other hand, the school cannot do nothing and risk appearing to support premarital sex.
I think that the ideal solution would be to suspend both the boy and the girl in question for the duration of the pregnancy. They could do their schoolwork from home and have some time to reflect on the consequences of their bad actions.
Whether that ideal solution is practical is another question entirely.
I think trying to compare this situation to the situation of an unwed adult pair is not productive as adults are no longer under their parents’ authority etc.