If there is matter in the universe it must necessarily exist, since the premise that there is matter in the universe can only be satisfied if the universe itself is there. This is somewhat tautological, and the answer is based on an interpretation of the term "existence" as synonymous with "to be".
That being said, one could state that the universe didn't exist, and given the absence of observers, no observation suggesting otherwise could be made.
I guess it amounts to deciding whether there is matter in the universe, though this of course cannot be done in the absence of observers ("life") either. It seems this makes the question a bit even more hypothetical than at first glance.
I agree, that the question is a little flawed. But it's also perfectly reasonable. Flawed in the sense, that it depends WHAT universe, your talking about. In my opionion, there's different versions of the word. I Could be the only inhabitant of my universe, in that, Do i know or care what happens in the life of the guy that lives on the other side of town? I'll never meet him, and his life will almost certainly NEVER interact with mine. Then there's the Universe we look at as a human race, The thing that our planet floats through.
And as for the perfectly reasonable part of the question: Both situtation above CAN be answered as a yes. Simply because our LIVES can be considered OUR universes. And on cosmic level, even if our Solar system really is just a glass marble in some giant figure's pocket, this being's world COULD be called the Universe.
Mind you this is just my opinion AND my first post to this board =) Feel Free to tear it apart, as it's the only way to learn