I think the answer is that he can certainly confess his sins to the priest, but that he cannot receive absolution. Like the Eucharist, one of the significations/effects of the sacrament of penance is to perfect, or re-establish, one’s unity with the Church. Unfortunately, those who are separated from the Church, and not actively seeking to be officially reconciled to Her, are unable to receive this grace, and these sacraments are consequently withheld from them. (One way to think of it: since your boyfriend is not yet a Catholic, ordinary honesty would prevent him from seeking to express a false unity with the Church through the sacraments.)
Such at least is how I would reason about this situation. You could do a lot worse than asking your parish priest about this though.