Can a person suffering with schizophrenia not have delusions, just hallucinations?

Yes: It is possible, especially early on, to have hallucinations without delusions.

Possible: Possible, but other symptoms need to be present.

Yes They Can: According to the diagnostic and statistical manual of mental disorders (dsm-iv-tr), to be diagnosed with schizophrenia two or more of the following symptoms must be present: delusions, hallucinations, disorganized speech, grossly disorganized behavior, and negative symptoms such as a blunted affect or avolution. So the answer to your question is yes. Other criteria exist for definitive diagnosis.