Can App Studio be configured to pull metadata from images submitted through the app and store those metadata as attributes of a point feature, such as a photo's date-time and location?
Yes definitely possible. AppFramework (AppStudio's Framework) provides a ExifInfo QML type, which can be used to extract metadata from images. And you can even write some data into images. This info can easily be written into Feature layer attributes using ArcGIS Runtime or using REST API for Feature service.