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.
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.