My understanding is that 学校は行きます would mean: As for school, I will go there.
While 学校に行きます is: I will go to school.
But is this the first sentence ever used? Or even grammatically correct?
Yes, 学校は行きます is grammatically correct and natural. But this has a clearly contrastive meaning. The sentence implies something like this:
(I said I won't go to the dentist but) I will go (at least) to school.
As a basic rule, a contrastive-は replaces が and を, but attaches other particles such as に, へ, で, から and まで. Still, when a contrastive-は comes at the beginning of a sentence, the associated particle can be omitted with the aid of the context. We even have eel sentences (うなぎ文).
I don't think the sentence is strictly incorrect from a grammatical point of view, but I doubt anyone would say it.
On the other hand, what is definitely used is the following:
You would add the は without dropping the に if your intention is to highlight that you specifically go to the school (as opposed or in contrast to somewhere else). But に is still required for this to work.