The issue with the cloud notebook is known and reported (nothing you can do about it).
Maybe this:
Do[ CellPrint[ Cell[BoxData[ CounterBox["Section", CounterFunction :> Function[Part[{"4.1", "4.6", "4.16"}, #]]]], "Section"]], 3]
It worked!
Edit: for some reason, the cloud notebook isn't displaying right. I don't know what you have to do to fix that.
