They have a public facing API described here:
https://developers.google.com/picasa-web/docs/2.0/developers_guide_java
You are right. You will have to authenticate your app using OAuth and then send HTTP requests using the provided API's.
It should work on Android. If you need a sample on how to use restful web services on Android, You can see this sample from google:
It's a sample app that uses the flickr API to stream photos.