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?
By the looks of it Google Photos is based off the same system Google+ handled photos which was through the Picasa Web Albums Data API.
EDIT: So I came across this question while trying to develop something using Google Photos. Currently I am working on an application that will transfer stuff from Dropbox over to Google Photos.
I can confirm that Google Photos does indeed use Picasa Web Albums API. The API is simply a data storage for anything related to Photos. Drive and Google+ make use of the Data API to persist photos. Looking at picasaweb.google.com you can see it redirects you to Google+ and shows a collection of all of your photo.
You can actually experiment by looking over the Protocol Guide You can further experiment by using the OAuth 2.0 Playground through the Picasa API.