My former T was on Facebook, but it never occurred to me to ask to be Facebook friends. I don't think she was on Facebook when I was her client. She was in her early fifties then, and it was back when Facebook was almost exclusively college kids.

My current T is on Facebook, and I am 100% sure she would not agree to be FB friends, now or ever. I think she needs separation between her work life and her personal life. Plus I think it could be complicated or confusing to "see" her in that context. She is in her forties now.