Welcome to the Esri Forums. Please be sure to always specify what version of ArcGIS you are using, and to completely explain your question (since 3rd party tools are uncommon in this space).
After a quick google search on terrasync I found this. Chapter 5 page 131 seems to indicate that pathfinder office is the package you need to export your field collected data. The point being that if you were to export the data, you could then use the feature class attributes for the basis of a geodatabase feature class. You may want to try a similar search online; perhaps the specific answer you are looking for is out there. Somewhere.
I realize this is quite old but there is a way in Trimble Positions Desktop Add-In to Export your DDF file to a complete gdb including domains. The schema design needs cleaned up a bit after export in my opinion but you do get a complete working gdb.
