Well, it's weird to ask if I agree, since I can agree or disagree for any reason, including no reason at all, and I imagine that's not what you mean to ask.
It's not clear to me whether you are requesting argumentation regarding the extent to which his thesis could have been construed to be true at the time, or at the current moment. I feel that since you're asking whether I agree--as someone living right now, that means that my agreeing or not agreeing has to conform, to some extent, to my other ideas, which are influenced by contemporary knowledge. After all, people do tend to avoid cognitive dissonance (though, as a neuropsychologist, I must add that people are also completely fine with either giving themselves bad excuses or not dealing at all with cognitive dissonance).
But I digress. Regarding your question, I would call attention to one of PBS Space Time's newer videos discussing the ontology of time and space. My answer will largely be based on content from this video.
One thing I'd call to attention is that some historic people, including Newton, famously believed that there was some sort of objective coordinate system through which we can appreciate the position of any given thing. It doesn't seem to me that Aristotle is arguing this position. Instead, he seems to be arguing that our ability to observe the "position" property of objects is dependent on our capacity to position them ourselves in a map inside our minds. In this context, the lack of any meaningful construct that would serve as parameter from which any sort of coordinate system could be established--cognitive pause to process; anyway, the lack of any such construct would make it impossible to localize the sky anywhere, and as such, it could be said that it is not anywhere.
As you say, though, he has to mean 'universe', here, because it's immediately clear that this is not true for the sky. Now... it's not clear to me that this is true for the universe, either. As I said, from Newton's position on this issue we're led to believe that this was a position that at least some people held, and it seems clear to me that Aristotle was not confortable with a completely relative positioning system (e.g., 'the sky is outside the Earth').
So, I hope I don't dissapoint when I say I have no position in this matter whatsoever.
tl;dr: I have no idea.