Some more details about the errors you encountered:

- **`Data selector user:hybridauth:profileURL for parameter data is invalid.`**

  Using the Rules Event like you're using, there doesn't seem to be something like `user:hybridauth:profileURL`, which I believe explains this error.

- **`The selected data property doesn't support writing.`**

  To understand the reason for this error, have a look at:

   - The question about "http://drupal.stackexchange.com/q/69728/39516".
   - The Rules issue titled ["The selected data property doesn't support writing." when Action: Set a data value is applied to a taxonomy field:tid][1].

With that, I'm fairly sure that the answer to the "***Is it even possible***"-part of your question is:

> **I'm afraid it is NOT** ... Though I'd love to see anybody tell me I'm wrong.


  [1]: https://www.drupal.org/node/1080660
  [2]: https://www.drupal.org/project/hybridauth