떠들다 only applies to verbal noise. So 떠들면서 춤을 추다 implies that they are either talking, laughing, or shouting while they're dancing. If people make noise some other ways, there are other expressions for that. 쿵쾅대다/쿵쾅거리다 = to make banging or bumping noise, especially with the feet. 우당탕대다/우당탕거리다 = to make a sudden and loud banging or crashing noise. 시끄럽다 (a) = noisy; 시끄럽게 (adv) = noisily. (applies to both verbal and non-verbal source) e.g. 손님들은 바닥을 쿵쾅거리며 시끄럽게 춤을 추었다 = The guests danced noisily stomping the floor. 가게 안은 북적거리는 손님들로 시끄러웠다 = The inside of the store was noisy with people moving around. (북적거리다 = a large number of people busying around in a place).

떠들다 means "To speak noisily in a loud voice." The word 떠들다 is used if the speaking using words with some laughing, spoken by a person or a group of people, is heard as a loud noise for people around the speaker(s). So, 떠들다 has negative nuance. 떠들면서 춤을 추다. means "dancing while uttering noisily"

it only means talking loudly