I know this is a stretch but would it be possible to store images on Google Drive while still running ZenPhoto on my current server?

Second part to this question, could ZP run on the Google Cloud Platform. https://cloud.google.com/

No http://www.zenphoto.org/news/using-external-sources/
Maybe via symlinks but Zenphoto is entirely filesystem based and for self hosting. It surely would cause speed issues.