The Church teaches that the desire for baptism, whether explicit or implicit, saves those who die before they can receive it. Yet, someone may ask, “If that person doesn’t receive the sacrament of baptism, is he ‘fully Catholic’”?
If by “fully Catholic” one means “getting to heaven,” then the answer is yes. However, if by “fully Catholic” one means receiving the character/seal of baptism, then the answer is no. The Catechism teaches that the desire for baptism “brings about the fruits of baptism,” but “without being a sacrament” (CCC 1258). Since the character is only communicated through the sacrament (CCC 1121), it follows that the desire for baptism does not communicate the sacramental character or seal.
What’s the significance of this? For this life, it simply means that the person wouldn’t enjoy the “rights within the Church” to participate in aspects of the life of the Church, such as the sacraments (CCC 1269). The character/seal is ordered to making the baptized “share in Christ’s priesthood” and constituting them as “a member of the Church according to different states and functions” (CCC 1121). Or, as Aquinas puts it, it gives a person the right “to do or receive something pertaining to the worship of the priesthood of Christ” (Summa Theologiae III:63:6 ad 3).
Concerning the afterlife, this lack of the character might not have any significance at all. The Church only definitively teaches that the seal remains at least until death. Even if the character does remain in heaven, which is the general theological opinion, that would only imply that the souls without it would experience beatitude in a lesser degree than those with it. But that’s not a problem because every soul will experience different degrees of beatitude in heaven depending on their state of charity.
Regardless, the important thing is that the baptism of desire does indeed save. And in that sense every soul in heaven is “fully Catholic.”