Would it be fair to say, with adhd, the childhood physical hyperactivity turns to mentally hyperactive as adults?

Not ncessarily: As the frontal lobe matures individuals with midler adhd may experience reduced restlessness and impulsiveness, but this may well remain present in more severe cases. Some individuals will also show some greater abilities to maintain focus, but adults wiht adhd still tend to change jobs more frequnetly, drop out of school sooner, etc. Classically difficulties with organization are more prominent.

Adult ADHD: Sure. Can turn into difficulties with organizational skills & task completion at work.

The natural course: Of adhd -combined type is that hyperactivity/impulsivity changes to an inner sense of restlessness. Teens & adults may still fidget by tapping/clicking pens, jiggling their legs, or getting up during classes or meetings. With updated neuropsychological testing for diagnosis, medication + cognitive/behavioral therapy + environmental manipulations through ada accommodations are available.

Slightly different: Main issue with adhd is the attention deficit. They are not paying attention enough to focus so they move from activity to activity. So they appear hyperactive. With age and self control, if the person can train himself to slow down and focus, they will usually turn out into mentally hyperactive and thriving individuals. But they need help as children to identify their weaknesses and to modify.

No: As a person with ADHD grows up, the symptom of hyperactivity is likely to disappear but the inattentiveness persists in about 50%. Some with extreme impulsivity may find symptoms persist but if you are wondering about hyperactivity, it is likely to fade.