I've googled my therapists/Pdocs over time; i think it's just curiosity and to make sure that i can trust these ppl. I've also hung around my old T's office (when I was still seeing her) which is right next to this park where i go to think things thru. I never told her cos i didnt want her to think i was some wierd psycho stalker and stop seeing me - fear; i was too scared to tell her.
I think it's up to you if you mention it or not; if you are brave enough, i think it will be helpful to explore why you needed to know more about T/seek T outside of session. And I seriously doubt that you would be terminated for one time. If you cant bring it up, dont feel bad, i understand.
Take care

*Willow*