I have not been able to import DEM GeoTiffs with Mathematica.
I downloaded two different DEM files in a GeoTIFF format from Earth Explorer (https://earthexplorer.usgs.gov/), one from the Aster data set and one from the SRTM data set and tried to import them. In both cases Mathematica completed the import with no error and shows a reasonable GeoTiff summary, but the plot it shows is just a plain gray square:
One possibility is that the gray levels are not balanced correctly, but I have no idea how to detect and fix this kind of problem.