Will my dog's hair grow back after giving her thyroid pills? ?

My dobe was recently diagnosed with low thyroid. One of her symptoms was that her hair was starting to look sparse near her backside and she also smelled funny despite giving her baths. She has been taking her thyroid pills now for about a week. Does anyone know if her hair will grow back like it used to look? How about the smell? Does it go away once the pills start taking effect? And how long does it usually take?