A doe with a fawn will always hide the fawn and lead the aggressor away from the area and come back later to retrieve the fawn!!!! I think you would have to be extremely unlucky to be attacked by any stag in the wild although I'd hate to be stuck on the end of a red or sambar antler though...
the reason deer run so fast is that their normally the bottom of the food chain unless your grass but I wouldn't risk exposing yourself to a Stag during the Rutt after calling him in you might end up the first person killed by a deer!!!!
The other thing that could happen is it might run over the top of you while trying to make it's escape from the area????
I've learned that pleasing everyone is impossible, but pissing everyone off is a piece of cake.