Can a person be psychotic without hallucinating? Yes. The paranoids merely have "delusional ideas"; they see the same reality that we do, but interpret it differently, work it into their system.
Can a person hallucinate without being psychotic? Yes, as for example during the hypnotic state, under drugs, when ill with a high fever, poisoned -- for many reasons.
What is the relationship between hallucination and worldview? The German psychological notion (more accurately Swiss) is that each individual has a structured, idiosyncratic, and in some regards unique way of picturing or experiencing -- or whatever it is one does with -- reality. It now is universally accepted that reality "in itself," as Kant put it, is really unknown to any sentient organism; the categories of organization, time, and space are mechanisms by which the living percept-systems, including the portions of the brain that receive the "raw" sense data, require the imposition of a subjective framework in order to turn what would otherwise be chaotic into an environment that is relatively constant, with enough abiding aspects so that the organism can imagine, on the basis of memory (the past) and observing (the present), what the future probably will be. Continuity is essential; one must be able to recognize a good deal of the external world in order to function (this, of course, is why the name problem is real and not a figment of medieval imagination; the logos, the word, turns chaos into separate and different objects).
A good deal of this organization is done within the percept system itself; that is, by less-than-conscious portions of the neurological apparatus, so by the time the "self" receives the sense data it has so to speak been automatically structured into the idiosyncratic worldview. The self (or ego or some damn fool thing) is therefore presented with material a good deal of which originated within its own being, at one level or another. In the light of this, the idea of hallucinating takes on a very different character; hallucinations, whether induced by psychosis, hypnosis, drugs, toxins, etc., may be merely quantitatively different from what we see, not qualitatively so. In other words, too much is emanating from the neurological apparatus of the organism, over and beyond the structural, organizing necessity. The percept system in a sense is overperceiving, is presenting the self portion of the brain too much. The cognitive processes, then, in particular the judging, reflecting frontal lobe, cannot encompass what it has been given, and for it -- for the person -- the world begins to become mysterious. No-name entities or aspects begin to appear, and, since the person does not know what they are -- that is, what they're called or what they mean -- he cannot communicate with other persons about them. This breakdown of verbal communication is the fatal index that somewhere along the line the person is experiencing reality in a way too altered to fit into his or her own prior worldview and too radical to allow empathic linkage with other persons.
But the crucial question as to where, at what stage, these perplexing aspects, augmentations, or warpages away from the commonly shared view begin, is not answered by any of this. We are aware today that a good deal of what we call "external reality" consists of a subjective framework by the percept system itself, and that there are probably as many different worldviews as individuals... but how do unwanted, even frightening, and certainly not commonly shared "hallucinations" creep in? Up until the last three or four years it would have been generally agreed that these invasions of the orderly continuity of world experience beyond doubt originate in the person, at some level of the neurological structure, but now, for the first time, really, the body of evidence has begun to swing the other way. Entirely new terms such as "expanded consciousness" are heard, terms indicating that research, especially with hallucinatory drugs, points to the probability, whether we like it or not, that, as in the case of Jan Ehrenwald's paranoids, the percept system of the organism is overperceiving, all right, and undoubtedly presenting the judging centers of the frontal lobe with data they can't handle, and this is bad because there can be no judgment under such circumstances, and no interpersonal life, due to the breakdown of the shared language -- but the overperception emanates from outside the organism; the percept system of the organism is perceiving what is actually there, and it should not be doing so, because to do so is to make the cognitive process impossible, however real the entities perceived are. The problem actually seems to be that rather than "seeing what isn't there" the organism is seeing what is there -- but no one else does, hence no semantic sign exists to depict the entity and therefore the organism cannot continue an empathic relationship with the members of his society. And this breakdown of empathy is double; they can't empathize his "world," and he can't theirs.
Hallucination, mental illness, drug experiences of "expanded consciousness" are menacing to the organism because of the social results. It is obvious, then, what role language plays in human life: It is the cardinal instrument by which the individual worldviews are linked so that a shared, for all intents and purposes common reality is constructed. What is actually subjective becomes objective -- agreed on. So, viewed this way, sociologically and anthropologically, it does not matter where the hallucinations originate or even whether they are accurate -- but unique and hence unshared -- perceptions of "higher levels of reality unglimpsed ordinarily," even by the person himself.
Real or unreal, originating within the percept system or received validly by the percept system because, say, of some chemical agent not normally present and active in the brain's metabolism, the unshared world that we call "hallucinatory" is destructive: Alienation, isolation, a sense of everything being strange, of things altering and bending -- all this is the logical result, until the individual, formerly a part of human culture, becomes an organic "windowless monad" [a description utilized by Leibnitz]. It does not matter that his reasoning faculties are unimpaired; it does not matter whether or not he feels "adequate emotion," those being the two classic criteria by which schizophrenia was diagnosed. Actually it seems to be that neither is impaired; faced with the sense data presented him, the individual does as well with it as we do with ours, and the same goes for his emotional life -- he may display moods and feelings that to us can't be accounted for. But we are not perceiving what he is; the emotions are almost certainly appropriate in relation to what he perceives, i.e. experiences.