Making an album available offline "should" cache/download selected Google albums to your phone such that they are available even when you in airplane mode. Having said that - all my Google account photos seem to be available, whether I'm on or offline. Also, photos uploaded into Google+ remain private unless you explicitly indicate who you want to share the photo/album to among your Google+ friends/circles.
I've also noticed that my albums whether in Picasaweb or Google+ are available and accessible from either web-app.
Dropbox, from the Dropbox app, has its separate "camera upload" feature to copy your photos to your dropbox folders. Select a private folder to keep your photos private.
