This is a highly subjective thing, so I can speak only for myself, but I notice I tend to take people more seriously if they post their real name and a photo. This has consequences on my behaviour, at least when they ask questions:
I will be more reluctant to downvote
I will show more patience with imperfect questions
I will have an increased willingness to add helpful comments, stick around, and provide additional guidance on how to improve the question.
I guess it is out of the feeling that someone showing a photo of themselves (well, supposedly) is willing to invest something in the community, instead of just drive by and get a quick answer for something.
With prolific answerers, I think it doesn't matter that much - the answers speak for themselves. I don't think a user with good contributions will be taken any less seriously just because their avatar is a lizard. Or even the default gravatar.
Can we measure (maybe with some facial recognition software) how well users with a "face" profile picture do better (or worse) than people with a default graphic?
Maybe, but any results you may get would most likely be spurious... even if the data show a connection between profile photos and some measure of success, you can always argue that those who post a photo of themselves are likely to be more invested users.