Umm, yeah, I've done that. I got quite obsessed with T a few months in and googled her constantly, I've done this previously with other professionals eg college tutor

Nothing particularly showed up, and I stopped doing it, but I did it again recently. Something came up which was personal and sad for my T. I felt so bad that I had invaded her privacy (I know it is in the public domain, but I'm sure she would not have intended it to come up on a search) and I felt awkward that I knew this information

I didn't mention it, and I won't. In my opinion, it's her business and nothing to do with me. This happened a few months ago and I don't really think about it at all now. But I don't google her anymore!