Can Livestock Guardian Dogs be used with herding dogs? Does the guard dog think that the herding dog is trying to hurt the stock and become protective? Do they accept the herding dog? Do they have to learn that the herder is OK to have around?
I've never read anything about using the two types together, but I would bet my last dollar that somebody on FR knows all about this.
Apart from that, unless a part of the herd sounds the "alarm" (which I don't think it does when the herder is around), the livestock dog will keep dozing.
Just my uninformed opinion.