What I have in mind is something like these two examples below:
Also, if it is not possible to create a 3D choropleth map in ArcGIS, is there some other GIS software package that can draw 3D choropleth maps other than Maptitude?
ArcScene is the ESRI approach to doing this. It is likely installed with ArcGIS so you should find it in the start menu.
This is a typical ArcScene map. Basically your attribute value can become the extrusion, you often need to normalize data.