When you say a single episode, are you talking about an episode of mania? The DSM-IV (Diagnostic and Statistical Manual of Mental Disorders) states that criteria for bipolar I disorder is the occurrence of one or more manic episodes or mixed episodes. Usually the individual has also experienced at least one episode of major depression, but this is not mandatory for the diagnosis of bipolar I disorder. Bipolar II disorder is characterized by at least one episode of hypomania (just a little bit of euphoria or irritability) and at least one episode of major depression. In other words, in order to have a diagnosis of bipolar I disorder you have to have experienced a period of intense, unexplained, crazy out-of-control, often irritated and agitated euphoric behavior. Because of the less intense manic episodes with bipolar II, one must have also experienced major depression to be given a diagnosis of bipolar II.
So to answer your question directly: Yes. If someone has a single episode of mania, this person, by DSM-IV standards, could have bipolar I disorder. This would especially be the case if this person has many bipolar family members as this is an inherited condition. Bipolar disorder is a cyclic illness; it’s very possible to feel “normal” during periods where the illness is at an ebb—especially with bipolar II.