There is no direct option to check in/out files into Vault through HyDraw CAD due to Autodesk limitation on use of Vault with AutoCAD OEM (on which HyDraw CAD is built).
But, it is found that with Vault Workgroup 2016 using the Vault Explorer, the DWG files could Open, View, Check In and Check Out with HyDraw CAD.
While Check In, you will get the following message, though the Check In will be successful.