We adopted a 5-1/2 week old, Peaches, and she used to suck on my neck. She did it all her life whenever she was feeling insecure or frightened. I never chased her away but let her "nurse" as we called it. She died at 17 years and we miss her still.
I should have clarified that statement...she was 17 years old when she died and has been gone nearly five years. We now have a 7 year old dog, Rosie, adopted from PAWS, and two sweet cats; one 13 years old and the other a 'kitten' about 5 years old.