I am using Arc Map 10.4.1.
I have the impression that my version of ArcMap will not perform vertical transformations/projections on datums but only the Pro version is capable of this. However, I also see that inside ArcMap a reference is given to "ArcGIS Coordinate Systems Data installation package" as a required data set needed to perform vertical coordinate changes. Also, a coordinate video by ESRI gave me the impression that ArcMap can do vertical datum changes. So I have to ask, if I download the data installation package, will that allow me to use ArcMap 10.4.1 to perform vertical coordinate changes?