Now I am trying to add the e-mail address as Account alias to a Hotmail Microsoft account, using https://account.live.com/AddAssocId.

I mark “Add an existing email address,” enter it, and click on the Verify link inside my Gmail inbox for the address.

What I get then is https://account.live.com/error.aspx?errcode=1086, stating “There's a temporary problem with the service. Please try again. If you continue to get this message, try again later.”

Adding a different e-mail address (that has never been a Microsoft account on its own) works, including verify link.