You can do some operations with SolidWorks files without opening only through document manager. Unfortunately, document manager do not have an api to save documents.
You can silently save document by opening a session of SolidWorks and turn the visibility off: ISldWorks.Visible = False. This will be a bit faster than opening the document and sawing it; but still time consuming since all data need to be loaded.
Another way is triger save as PDF for your current document on some events like saving.
Hope this helps
Sorry if this does not answer your question directly.
Rather than using API, you may be able to use the Solidworks task scheduler.
1. Open task scheduler
2. Select export files
3. Select Add folder and add folder containing drawings
4. Set time to run task
Technically, this does open files, but may be worth investigating if you can run it after hours.