I am a bit surprised at this. If I can connect to GDB files in Trimble Business Centre and a freeware like QGIS, why not Civil 3D?
The route via shapefiles does not work. Shapefiles have a "Number of Characters" limitation (max 10 characters). So when you convert GDB file to Shapefiles, the attributes get truncated to 10 characters resulting in duplicate attributes and get rejected. So, that is NOT a robust work around. It may work in some cases though.
AutoDESK has a relationship with ESRI. (We can export to FGDB format !!). AutoDESK should, in the interest of their customers enable connection to GDB files. Afterall ESRI is developing competing CAD software and promoting the same.
CAD, GIS and Survey Softwares can no longer survive in silos. Those days are over.