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.

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 "https://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.