You need an internet connection to install Datashare.
You also need the internet to find people, organizations and locations in documents the first time you use any new NLP option because the models which find these named entities are downloaded when you ask for finding named entities the first time. Subsequently, you don't need an internet connection to find named entities after.
You don't need internet connection:
to add documents to Datashare
to find named entities (except for the first time you use an NLP options - see above)
to search and explore documents
to download documents
This allows you to work safely on your documents. No third-party should be able to intercept your data and files while you're working offline on your computer.