I think it depends on the child.
DD has maintained 10-14 hours of dance, plus being in 2 school sports teams with fixtures and training, throughout her time at secondary. She is now in Y10, managing coursework-heavy GCSEs (Art and Textiles) and D of E as well (though much of that is based around her dance school - so she helps with younger classes etc).
She is bright, driven, and phenomenally organised. Luckily, most of her dance hours are during the week, so she does have much of each weekend to catch up and spend longer on her art homework.
DS has had more of a portfolio of activities - sport of different types and music. He now does as many hours of music as DD does of dance, but it is condensed into fewer sessions, so he has 'nights when he works' and 'nights when he plays music'. Again, weekends are when he catches up, and it helps he no longer plays club football.
I would say that it has helped them both socially and organisationally, and it has made their potentially problematic 'teenage years' very smooth as they have simply not had time to get involved in any activities that could get them into trouble.
However, they do both find academic work fairly straightforward. A child who really really needed to work at every lesson and every homework would possibly need to cut back in terms of hours.