The state of Missouri allows any legal method, including archery to be used during the firearms seasons. As long as the hunter orange requirement is adhered to and the proper firearm deer tag is used. You cannot bow hunt on an archery tag during rifle season, it must be a regular firearm tag, and then you can use anything from rifle to crossbow, and even an atlatl if that's your thing.
This is the way it should be in my opinion. As long as you purchase the proper tag, then why not let the person chose their weapon?
I'm all for it, and I personally know a few who do use archery tackle during firearm season, mainly because that's the peak of the rut and they don't want to miss out, or put their bow down to wait until the 11 day rifle season is over.....especially if you have that monster buck patterned down to a specific area and only need a bit more time to nail him.
After the initial 11 day firearm season, archery season picks right up immediately afterwards. Then continues right on through till Jan. 15th.