Is it Islamically permissible for a young man and a young woman studying abroad to contract a marriage without their parents' knowledge, in order to protect their chastity, on condition that the young man formally propose to the young woman a year later?

If there is no valid Islamic marriage contract between them, then she must repent. The best solution is for him to convince his father to arrange the marriage contract for him through a valid power of attorney from him to someone in the father's country, or by the father authorizing someone to act on his behalf in the contract.