You bet they do. I had one of my daughters do something similar the day after her 4th birthday, which thankfully falls in August.
She took the ten dollar bill she had gotten for her birthday, and while I was tending her infant sister, strolled the half a block down the street to the drug store, purchased a roll of Necco wafers, and strolled home, with the candy and nine dollars and seventy-five cents in change in small brown paper bag. Oh, and she was wearing only her panties. Needless to say her teen years were a nightmare.
This woman is now a nurse in the ICU, and has a daughter exactly like her.
That is one of the funniest stories I have ever heard!