I usually carry on milking my females until around 8-10 weeks before kidding - by that I mean, I will have been gradually drying them off up to that time. Starting with two weeks of milking once a day, then every other day and so on .......
You do need to continue milking while they are running with the billy, otherwise you will have some uncomfortable goats. Even if the female is just served by the billy, and not run with him, the smell is not good, and sticks to everything ......so possible the milk could have a funny taste too. So, if billy runs with the female it will more than likely be worse!!