Yes, I have confirmed that the NoData values are not in the source data, only in the mosaic. I'm aware of the location of the actual holes in ArcticDEM data in my study area. There are none in the area I'm currently working on. It is also not an issue of overviews not being correctly built because the explore tool returns a value of NoData, not a legitimate value but with nothing displayed visually.
NoData in the source is -9999, NoData in the output is 3.4e+38 by default.
This data is being used for surficial geology research, and the research scientists I support prefer to have the data as a mosaic. I will be generating a hillshade from it, and it is also used for extracting local topography statistics for landforms of interest.
I know that this is an ArcGIS problem because QGIS creates the mosaics without issue.