Is there a setting to get Craft to save user photos to S3 like a regular asset source?
Craft 3 Update
This is currently possible in Craft 3. Install the AWS S3 plugin from the Plugin Store. Make sure you're running Craft Pro. Create a new Asset Volume using S3. Go to Settings->Users->Settings in the Control Panel and set the "User Photo Location" setting to your S3 volume.
Currently no, although this is likely to change in the upcoming Craft 3.