Usually a "good" T won't make the first acknowledgement, but if the patient does the recognition and approach (such as a smile or nod) the T will respond. Ts are human and do human things like go outside of the office.

They have plenty of other friends, so no one will know that you're a patient or a friend if you don't say anything but," Hi good to see you how are you doing?" Like regular conversations that are just friendly greetings.