Is it possible for bipolar disorder to be mistaken for adhd?

Absolutely: They share many of the same features of distractibility, inattention and hyperactivity. Many patients diagnosed with adhd are later understood to have bipolar disorder after the mood symptoms are properly illuminated. Further complicating the picture, bipolar disorder is associated with a neurocognitive impairment that can look like adhd. The distinction is important because treatments differ.

Yes and vice versa: There is a lot of overlap. Mania leads to impulsivity, increased thought process, and possibly increase in activity. Depression leads to pervasive negative thoughts and indecisiveness which interfere with attention and productivity. It may be difficult to sort out, but with BP d/o there are usually periods of "normal" mood and behavior whereas adhd is persistent.