If I'm understanding your question correctly, simply saving a document in a user's home folder on a local machine does not transfer it between machines. Open Directory is only going to authenticate your user's credentials and grant them access to the machine.
You can, however, setup preference and file syncing with Workgroup Manager. You can download it here: http://support.apple.com/kb/DL1567
Once installed, configure it to connect to your server with your diradmin account. Once authenticated, you can setup file syncing to sync an entire home directory or just folders within it, preference syncing, etc. You can also manage preference for users and groups and enforce company policies regarding security or whatever else you may need to. It can also automatically mount the user's network home folder when they login.
Once you set this up, whenever a user logs into their account on a managed machine, it will run the preference and file sync settings you created.
I hope this answers your question. Or at least gets you steered in the right direction.