Solution

To display drillholes in Discover 3D, the drillholes and associated data must be part of a Discover
Drillhole Project. To create a Drillhole Project, run the Drillholes > Project Setup tool in Discover.

You cannot open a drillhole proejct directly in 3D, it must be firstly opened in Mapinfo Drillholes menu, and then 

"pushed" to 3D using the Mapinfo Discover3D>View Drillhole traces option.