It depends on the nature of 'could'. How do we know anything could be? This is a central preoccupation in the epistemology of modality. Modality is the study of necessity and contingency in the truth of propositions, and is related to metaphysical presuppositions related to possible world semantics.
Ever since the linguistic turn, it is customary in philosophy to heartily appraise the use of language in a proposition or interrogative for possible insight into the question. In this case, before answering truthfully the question:
Could there be a universe where the concept of order and logic and numbers and objects and space and time don't exist?
one must simply understand ideas like possibility, concept, universe, and existence. This task requires committing to value-laden propositions of both epistemological and ontological sorts. Congratulations, and welcome to metaphysics!
Let's start with the obvious one. When you say possible world, do you mean an actual physical plane of existence? Or are you more like me who views a possible world as a data structure laden with variables, a mere potential representation of a thing-in-itself? The first position which was championed by David Lewis in his On the Plurality of Worlds, and the latter is more inline with Kripke's views. There are many people who accept the many-worlds interpretation, that there is no collapse of a waveform, but rather there are infinitely many physical worlds. What about the basis for determining possibility? How does one decide what is possible and what is not? Do you prefer modal realism to modal rationalism? And then there are questions of existence (the astute reader will see the existential declaration!). What are your views on ontology and meta-ontology? Quine? Carnap? Meinong?
Until you examine your own ontological commitment and other metaphysical presuppositions, it will be mighty difficult for you to embrace a position on this question.