Whether they "are both of legal age to engage in sexual relations" has no relevance to the legality of "shacking up." If their parents are ok with it -- and if they can find a landlord willing to rent to two unemancipated minors (which is probably the most unrealistic part of this, unless the OP is envisioning some sort of alternative living arrangement that doesn't require paying rent to a landlord) -- then they may legally live together, regardless of whether either or both is older than the "age of consent."

