Could untreated depression turn into bipolar or a psychotic disorder?

It may. Why it may, is based on the fact that depression can precede or be a part of bipolar disorder that is in the depressed mode and hypo-mania or mania may follow. It may also be that the depression becomes so severe that the depressed person becomes psychotic. Ptsd folks can have a psychotic depression as well. Brain trauma can cause a psychotic depression as can alzheimers dementia.
Quite common. Depression is frequently the first symptom of bipolar disorder and may precede mania/hypomania by months or years and therefore the diagnoses of bipolar disorder may be overlooked. It may eventually progress to mania and in severe cases have paychotic symptoms a well.Depression and psychotic symptoms may coexist in severe unipolar depression particularly in the elderly.