After some looking, there is a way, to do this and you don't even need 3D Analyst.
ArcToolbox>Conversion Tools>To Geodatabase> Feature Class to Feature Class
Under the Environment Settings, set the Output Has Z Values = Enabled
Set Default Z Value to whatever.
BTW. The Feature Class to Feature Class tool is available in ArcCatalog by selecting Export from the context menu after right-clicking on the feature class.