Mine did not. Actually he rarely even looked at me- or, he did- but we rarely had eye-contact. He closed his eyes when I tried to glance at him after I had said something I wanted to see his reaction to.
That might seem odd, but it had its reasons.
I needed a space totally free of judgement and/or opinions at that time. I just needed a space with no rules other than the freedom to speak.

I do miss him, maybe I will go back sometime in the future.
Now I am seeing someone because I am in the process of getting diagnosed. (Last time I just wanted someone to talk to)
He always smile and we have eye-contact whenever I look at him. I am not so good with eye-contact, I am pretty much all over the place.
I don’t know if he hugs, I don’t like that- so it’s not something I have the answer to. We have shaken hands the first time.
It looked like he was gonna do it the second time aswell, but I prevented that by greating with a head-nod and a smile instead.

I miss my former one, but I do like the one I am seeing now. But it is short term, after diagnosing me I am getting a new one… Oh well, I’m gonna give it a shot. If it doesn’t work out I can always call my former one.
(Private, so more expensive)