A few years ago, I received an email from the dojo Secretary of a dojo in England. It said that their teacher was visiting relatives in Houston and they were asking if he could practice with us over the weekend. I looked up his name on Google and found out it was Terry Ezra, 6th dan, Aikikai. After checking around, I responded that he was not only welcome to practice with us, I insisted that he teach all the classes that weekend if he wouldn't mind. They thanked me and he did come to the dojo and taught all the classes. He was wonderful in his Aikido and we took him out to eat dinner and got to know him. He insisted not to be paid so I gave him a thank you card (and paid him anyway). We now have him come and teach us every year and look forward to it. He has been really good for us and demonstrated a protocol that made everything easy and introduced no complications for us.
Yes, by following the correct protocol you can go from being strangers to being friends. That is one of the reasons why a basic understanding of these things is important. I sometimes see dojos where etiquette is sloppy or even non existent. They may be happy but their people can't go anywhere without causing offense.
Saotome Sensei once went to teach a seminar at some dojo. When he walked into the dojo, one of the students (someone who should have known better) yelled across the room, "Hey Saotome! How are you?" Sensei said that for the whole weekend that person didn't exist; he was a non-person as far as Sensei was concerned. Of course, that sort of behavior isn't polite in any culture. It's just sloppy behavior. "Rei" is about not being sloppy.