Off the top of my head I recall reading about 2 home invasions where the homeowner used a shotgun, both involving 2 or 3 attackers and resolved with one shot. The attackers in both cases fled, IIRC. One involved an old lady using bird shot. They caught the suspects in that case. One of them was wearing a leather jacket and the shot didn't penetrate through. I don't know what the defender in the other case was using, though I believe he did wound one of the attackers.

While this is a very small sample size, I, personally, would not trust bird shot even at home defense distances. From what I've read, #1 or #4 buckshot seem to be recommended as being a good balance between effectiveness and mitigating the risk of overpenetration/penetrating walls.