I had a cvs - not for a nuchal fold result but for a previous chromosomal issue in my DD. I found the cvs not particularly painful but just a bit emotional. The pain lasted maybe a second or 2 as they use local anaesthetic as deep as they can. Waiting was the hardest but I think my wait was longer due to the specific test they were doing.
I just rested that day and the day after I think but had no bleeding or pain afterwards.