I think that the named references will always get in the way & stop multiple parts being imported/exported in this way. Also assemblies refer to the database part & not native part. There could be a way round both the problems but I haven't had much chance to look.
Garys solution to...
There is an option in Teamcenter to 'export file on check-out' in the options under General>Check-in/Check-out. Specify a location to put the file on your local drive and tick the 'Remove file on check-in' as well as it can get messy in the check-out folder.
When you check-out CAD data the file...