I would think so. You don't care to take a side because you have no knowledge of whether either side is correct. Sounds reasonable.
I beg to differ, among other reasons because I happen to consider myself both an apatheist and an agnostic (I'm a sucker for funny words, I know).
Let's go at this piecemeal.
Do I care to take a side? You could say so. But my apatheism is more in the sense that I don't care whether there is a god or not.
Not quite the same, because taking a side is a secondary consequence. The true focus is on whether I mind if there is a God or not.
Do I have knowledge about the existence of a God? Not in a true phylosophical sense. I have no satisfying argument or measure with which to truly seal the matter.
Still, it seems to me that you are trying to say that apatheist agnostics (of a different variety from mine) may well exist, despite agreeing that those are incompatible stances?