"They drink tea and chat at the same time."
他们一边喝茶一边聊天 should be an acceptable translation, the English "they" does not have a gender.
I think it’s ok if you come from the English sentence. But be aware that usually the first action is interpreted as the background for the second one. So your sentence would correspond to English “They drink tea while chatting” while the model translation would be “They chat while drinking tea”. In this case there isn’t much difference but in context one order is often preferred over the other.
Nothing in the English sentence tells us it's 她们 instead of 他们，please change. Thank you.
The wonky and awkward thing about this sentence is who doesn't chat as they drink tea with other people? Isn't that the entire point of tea? Why not just say, 'They would draw breath as they were working.'?