OpenID exists so that applications can use a large, well-established entity, such as Google, to handle user authentication so that the application developer can focus on other tasks. Your goal, based on your question, is to do exactly that, offload data storage concerns to a third party so that you can focus on your product and avoid reinventing the wheel.
However, OpenID doesn't work like this. The idea, as you know, is to outsource the authentication process, and only the authentication process, to the third party. OpenID is supposed to do no more, no less; it either responds with "yes, we know this person is who he/she says he/she is" or "No, I do not know this person".
To store application data in a Google account would sort of defeat the purpose of OpenID, and I can't see any OpenID provider breaking this standard.
Solutions to Your Problem:
With that said, I have two solutions to propose to you that, while they aren't exactly what you're looking for, they do in fact solve your problem and allow you to focus on building your product and your brand.
Bigtable-JS:
Bigtable-JS is a project maintained by Chris Thatcher. It's a RESTful JSON database that runs on Google App Engine. You need not know Python or Java to work with it, as it's designed to accept HTTP GET, POST, PUT, and DELETE requests to simply retrieve and store data in the highly scalable Google App Engine datastore.
The project hasn't been updated in 2 years, but considering it's just storing JSON strings, it's quite possible that maintenance is minimal.
Also, since your data storage needs are light, with the right amount of caching, it is quite feasible that you could operate without exceeding Google App Engine's free quotas.
This open source project is available on GitHub.
Blogger:
Is it safe to say that when most people think of Google Blogger, they think of blogs? Well, Brett Morgan and Pat Coleman, both members of the Google Blogger team, seem to think otherwise.
In their 42 minute presentation at the 2011 Google IO Conference titled, Google I/O 2011: Building a Business Web Presence using Blogger APIs, they outline how they use Blogger API's to build ecommerce and mobile websites, capitalizing on Google's infrastructure while also using tried and tested API's.
The websites they show in their demos look nothing like Blogger, and this is because they looked beyond blogs and instead took a more abstract approach to using the API's:
- Posts
- Post Title
- Post Author
- Post Date
- Post Body
- Post Tags
- Post Comments
These are really just groupings under the hood, and your app need not care whether it's storing data in a post body or some other text variant. The power of REST is in the layering that the interface provides between the two systems that frees them both up to simply do what they do best.
Since you're just storing a JSON string, you could conceivably store that string in a post body using the Blogger API's, and make the blog private so that the data is safely secured in Google's infrastructure.
Summary:
While neither of these solutions will allow you to store data in a user's Google Account, both of them offer you the freedom to focus your development efforts on other tasks and leave the database administration tasks to the cloud.
Other solutions you may want to consider are as follows: