You touch upon a good point here. Philosophers concerned with language, such as Kant and Wittgenstein, would likely argue that apophatic statements of what God is not require us to admit the following: by using apophatic language we consider God’s existence itself a necessary attribute of God’s ineffability.
However, as Kant argued, the language of “is” requires a predicate (the copulative verb links subject and predicate; it is not a predicate in and of itself). Therefore, existence is not a predicate and the ontological argument fails: it proposes that God’s being must be greater than the idea of God’s being, and that consequently God exists because God is maximally greater in reality than in thought (per Anselm).
The ontological argument becomes a tautology: “God is because we think God is.” Wittgenstein would argue that this is a faulty language problem. In reality, there is no problem at all. The primary contemporary question of the revisited ontological argument then becomes whether or not existence is an necessary attribute of God.
But as you have suggested about God-language: if God exists, we must be able to think about the possibility that he exists (the “apophatic” negative relies upon the “kataphatic” positive statement of God’s existence).
If we can’t think about the possibility of God’s existence, then God’s existence becomes necessarily incomprehensible (the apophatic here is simply an ontological argument expressed in the negative). God’s existence would be irrelevant.
It wouldn’t matter if God exists or not. We literally couldn’t hypothesize about God. Occam’s razor would apply to matters of necessary thought. And thinking about something ultimately incomprehensible becomes ultimately unnecessary (Where did the idea of God come from? … Who cares?).
Thus, the question of God’s existence raises the possibility of what Paul Tillich described: “God is the ground of all Being.” In other words, God does not exist as Being, but rather as something Wholly Other to which Being points: offering an explanation of why something exists rather than nothing, or why we differentiate diversity of thought as meaningful.
This might appear instinctively true because meaningfulness lies on a boundary marker outside of our symbol-set, and cannot be proven true in any sense per Godel’s incompleteness theorems. In some small empirically-minded way, it might be possible to know what we don’t know when it comes to hope in an open-ended future.