Thank you Bojan and Dan. Yes, I had already checked the help and the transformations pdf and noticed the transformation parameters were correct (and not null). But that doesn't mean that behind the scenes the software is actually applying the vertical transformation portion. In ArcMap, for example, the same transformation (ITRF_2000_To_ITRF_2005_1 and ITRF_2005_To_ITRF_2008_2) can be applied to a raster DEM with a defined HCS & VCS, but in reality (b/c ArcMap will only do vertical transformations on vector data, but not on rasters), only the horizontal coordinates are transformed and nothing is applied to the vertical. Out of an abundance of caution I was looking for confirmation that in Project Raster the VCS transformation from ITRF00 to ITRF08 is truly being applied in ArcGIS Pro 2.3.2 (without having to install any separate Coordinate Systems Data file), as this is an important part of the workflow for one of our projects.
On a second note, I just noticed in the Project Raster help that "This tool can only output a square cell size." Our data is in Geographic/decimal degrees, ITRF00 and is being transformed to Geographic ITRF08. The pixel size is 0.000006 x 0.000006 degrees (i.e., same dimensions in x & y), but in a linear sense the size is a rectangle, not square. So now I am confused. Can I even use Project Raster when working in a geographic coordinate system?? Help!