When I had mine put on, which was one crown on one implant, no pain at all and no injection needed. For me, they placed the crown on the implant, torked it in and took it off to make minor adjustments a few times. Once the dentist was satisfied, he placed it in, torked it in and then placed filing material over the screw to hide it.
the only thing I felt was slight pressure after the torking, but it fades away pretty quickly. They use a tool that ensures they apply the perfect level of force when they do the torking and stops when it’s tight enough.
I actually had a nice surprise that day. When I went to pay, I was informed that the lab cost was cheaper than what they had initially quoted for me.