No. You can allow secure PDF documents and HTML Products to be viewed off-line. All DRM controls (preventing copying, printing, etc.) are retained within the file itself and therefore no Internet connection is required to enforce controls. Please bear in mind however that an initial connection to the Internet is required to validate the user license and obtain the appropriate decryption key(s) when your customers view your protected files for the first time.
If the document / product is part of a publication then only the first file in that publication will need an internet connection. If another file in that publication is set to be viewed offline, then it will NEVER need to connect.
However, you can enforce that your customers connect to the Internet to view your documents / products if that is what you require.
If you choose to limit the number of views and/or prints, this will force a server check, even when the document / product is meant to be viewed offline.