First lets define our terms, particularly "Catholic".
By canon law a "Catholic" is someone baptized into the Catholic Church. Let's look at the relevant canons:
Can. 204 §1. The Christian faithful are those who, inasmuch as they have been incorporated in Christ through baptism, have been constituted as the people of God. For this reason, made sharers in their own way in Christ’s priestly, prophetic, and royal function, they are called to exercise the mission which God has entrusted to the Church to fulfill in the world, in accord with the condition proper to each.
§2. This Church, constituted and organized in this world as a society, subsists in the Catholic Church governed by the successor of Peter and the bishops in communion with him.Can. 205 Those baptized are fully in the communion of the Catholic Church on this earth who are joined with Christ in its visible structure by the bonds of the profession of faith, the sacraments, and ecclesiastical governance.
God, obviously, isn't baptized into the Church, therefore He is not a Catholic.
The Catechism of the Catholic Church defines a "Catholic" in paragraph 837 thus,
"Fully incorporated into the society of the Church are those who, possessing the Spirit of Christ, accept all the means of salvation given to the Church together with her entire organization, and who - by the bonds constituted by the profession of faith, the sacraments, ecclesiastical government, and communion - are joined in the visible structure of the Church of Christ, who rules her through the Supreme Pontiff and the bishops. Even though incorporated into the Church, one who does not however persevere in charity is not saved. He remains indeed in the bosom of the Church, but 'in body' not 'in heart.'"
God would not be a "Catholic" by this definition either.
You are thinking of it a bit backwards. God isn't a part of the Church, the Church is, in a sacramental sense, a part of God (His Body). The Church is the Kingdom of God, the One True Religion, The Bride of Christ, and the People of God, but God is not a member of Her, rather she is journeying toward Him.
We can't say that God is Catholic, but we can truthfully say that God wants everyone (yes, that means you too) to be Catholic.
|The Trinity by Masaccio (detail)|