Thank you, @Schillz, for your question and @Pål_Herman_Sund for your assistance.
First, the theory...
As @Pål_Herman_Sund already said, "WGS 1984 and the CGVD 2013 are two very different things." CGVD 2013 (WKID::6647) is gravity-related vertical coordinate system (datum). WGS 1984 is geographic coordinate system (WKID::4326) and vertical coordinate system (WKID::115700) with positions and ellipsoidal heights, which you natively get from GPS observations. The first realization of CGVD 2013 is through Canadian Gravimetric Geoid model of 2013 – Version A (CGG2013a) in NAD83(CSRS) and ITRF2008. This basically means that geoid undulations (difference between ellipsoidal heights and orthometric heights) are provided between NAD 1983 (CSRS) or ITRF 2008 ellipsoidal heights and CGVD 2013 orthometric heights based on positions in NAD 1983 (CSRS) or ITRF 2008 geographic coordinates.
To correctly transform between CGVD 2013 and WGS 1984 heights, it can be done in two steps:
GCS: NAD 1983 (CSRS) / VCS: CGVD 2013
<- - - vertical transformation with geoid model - - ->
GCS: NAD 1983 (CSRS) / VCS: NAD 1983 (CSRS)
<- - - 3D geographic transformation(s) - - ->
GCS: WGS 1984 / VCS: WGS 1984
Note, your CGVD 2013 height data must be in NAD 1983 (CSRS) or ITRF 2008 positions, so you can transform them with the geoid model.
Now, the practice...
In ArcGIS Pro, you can transform your 3D vector and raster data with Project and Project Raster tools, by checking Vertical checkbox in the tool. The vertical checkbox becomes available when you add 3D data to the tool and set horizontal and vertical output coordinate systems.
Unfortunately, we don't have any vertical transformations for Canada yet. Vertical transformation for CGVD 2013 is on our list, but some other projects came up and we haven't been able to get to it.