Is it proper for a wait person who is a casual acquaintance to sit down with customer w/o being invited to?

I don’t think it is proper and have noticed this going on more and more.
The last time I went to a restaurant with some friends, the waiter kept coming by and sitting down to chat for a few minutes. This went on through the whole meal. We were celebrating a birthday, chatting with each other because we hadn’t seen each other in a while and really didn’t welcome the intrusion. We were polite, but not really friendly. He didn’t get the hint.

Unless the waiter was invited to join your group in this way he/ she should not have attempted to join in.
However it all depends on how well you are acquainted with the waiter.
In a small town this is acceptable and even welcomed.
Usually the waiter asks permission first.
Sometime the waiter is tired and really needs to sit and get off their feet for small comfort even for a few minutes.
In this instance a ” I bet you must be tired after a long day”? would have helped .

Great first answer. As for the second, the acquaintance is so casual that the restaurant is the only place we know her from. And if she’s tired, she can go elsewhere to rest.

No. Not unless they are invited to take a seat by the people at the table.

It sounds very rude to me. I would be very off-put if that happened to me. But different cultures accept different levels of familiarity/presumption between customers and service people.
For instance, I have never known a waiter to introduce him/herself at a restaurant in France, and that is all but expected in restaurants in the U.S. now. (But then again, they have to hustle for their tip money here and many try to do so by being personable.)

It’s rude in my book, whether its the waiter or someone else who is not in the party to join unless their invited.

Having said that what if it was a well known celeb chef like Jamie Oliver we’d probably be thrilled LOL