Of course! The FBX SDK can read/write FBX (5, 6 and 7), OBJ, 3DS and DXF files without external help. The converter is only a UI on top of the FBX SDK. By default, when you call FbxImporter::Initialize without specifying the file format, it will auto-detect which file format it is and instanciate the appropriate reader internally. So basically, you could try calling import, then export but with a file format of your choice. File formats can be retrieved using the GetIOPluginRegistry on the manager.
Robert Goulet, FBX Dev Lead