Does the Google Photos app, released on May 28, 2015, have an API which allows uploading of photos? The app seems to build on Picassa and Google+. Can one of their APIs can be used to upload into Google Photos?
There's an official API for Google Photos now.
It contains an upload media endpoint. That section mentions that all photos uploaded through that endpoint are counted towards the user's storage limit:
Note: All media items uploaded to Google Photos through the API are stored in full resolution at original quality. If your uploads exceed 25MB per user, your application should remind the user that these uploads will count towards storage in their Google Account.