Do symptoms of depression increase or decrease the likelihood of having adhd?

Neither: Problems with concentration may be a component of major depression or adhd or both or neither. Adhd does not have as one if it's components a problem with someone's mood. That being said, the stimulant medications commonly prescribed for adhd can cause, as a side-effect, a disturbance of one's mood. That's why the diagnosis of adhd should not be made lightly and only by those most/best qualified.

Depression: Depression affects concentration and attention, but has no correlation with adhd likelihood.

Neither: 70% of the time adhd in kids & teens has a comorbidity, a co-existibg condition: oppositional defant disorder in 40-50% anxiety in 33%, depression in ~18%. If these are related to the harmful dysfunction caused by adhd, they often improve with proper treatment of adhd. Family history helps define this. If a child has mania, psychosis, or major depression, the adhd cannot be treated first.