I think it only works temporarily while the horse is pregnant and not cycling.
I believe that behavior during estrus is genetically linked. A mare who is very moody is going to likely have a filly that is moody as well. I have one mare who is obvious every time she is in season (and that seems to be the most likely time for her to act crazy and spook out from under me). She was bred once in her life, so I doubt breeding "calmed her" any.
I have another mare who if you didn't know better would think is a gelding. She shows absolutely NO signs of being in estrus... I know she is cycling, sometimes she might raise her tail if you brush over her rump. Other than that, you can't tell any difference. She has not been bred. She has some days where she is more nervous than normal, but I can't tell if she is just feeling good on those days, or if she is seasonal. She doesn't act different around strange horses. A nice riding mare!