sort of
Yes and no. Chimneys were never wide enough for an adult human to fit down, and certainly not one as wide as Santa is supposed to be. However, back in the days before the child labor laws chimney sweeps often used to employ young children to help them in the cleaning of chimneys by going down them. It was a dirty and dangerous job with very little pay, but somebody had to do it and unfortunately it fell to the defenseless little child to perform this act.
BTW There have been some recent stories in the news about adults who came down chimneys as a method of breaking and entering for the purpose of burglary. Unfortunately these dumb crooks have gotten stuck, and wound up doing time in the hospital as well as the jail cell