Yeah, it all depends what you mean by “Catholic.” It’s used in many different ways. But, in general, based on how the term “Catholic” is most often used, I think I’ll have to say that God is Catholic. (This is, of course, assuming that Catholicism is true … which I personally believe)
If you mean Catholic as in “one who is in full communion with the Catholic Church” then, yes, God would be Catholic.
If you mean Catholic as in “one who thinks the Catholic Church is the one true Church” then yes, God would be Catholic.
If you mean Catholic as in “one who knows the truth about Jesus Christ and his Church” then, yes, God would be Catholic
If you mean Catholic as in “one who acknowledges the truth of Sacred Scripture and Sacred Tradition” then, yes God would be Catholic.
If you mean Catholic as in “one who receives the sacraments” … you could also, I guess, say that God would be a Catholic. I think. Christ (in addition to receiving baptism, though that was not the same as our sacrament … depending on what you mean) definitely received the Eucharist … right? Last Supper? Sure, he never went to confession, because he never sinned, but tradition holds that the Virgin Mary, due to her sinlessness, never went to confession either, but would have received the Eucharist throughout her life. I would certainly say that the Virgin Mary was Catholic. With the same logic, you could say Christ was Catholic … and therefore God is Catholic.
If you mean Catholic as in “one who is a member of the Catholic Church” … it depends what you mean by “member.” It is said that Christ is the Head of the Body, and the Body is the Church. But is not the Head a member of the Body. It certainly is in biological parlance … so if we keep the analogy, then I would say Christ is a member of the Church … and thus God is as well. Correct me if I’m wrong, but the leader of a club is still considered a member of that club … right? However, if “member” comes with the understanding of subservience to something higher … then there’s an argument against this. Although doesn’t the Son serve the Father? Perhaps the Son (and the Holy Spirit?) are Catholic and the Father is not. (That’s actually pretty funny)
Now, to be fair, it is a pretty firm tradition that the Blessed Virgin Mary is the “model Christian” … and “Christian” literally mean "Follower of Christ." Christ is not a follower of Christ (b/c, I hope you see, that doesn’t make sense).
So, if we mean “Catholic” to be “a Christian belonging to the Catholic Church” then, no, God would not be Catholic. That definition, I admit, probably makes the most sense with regard to what we’re talking about. But, again, it depends what we’re talking about and how the word “Catholic” is used.