No you do not have to! The problem that cloud services is designed to solve arises when using keynotes across multiple locations or networks. Revit will read keynotes from whatever source is set in the keynote settings. If that is a text file on the local network it will read the notes from that path without issue. The problem is twofold if you are sharing the BIM360 project with multiple offices. First, you can’t edit the text file simultaneously in multiple offices; you would need to make changes in one office, send to the other, have the office make changes and send back, etc. Second the path in both offices is not likely to be the same in both offices, so the multiple offices will constantly be fighting over the path to the text file.
If you are only working on a single network you can still use a local text file to store and work with the keynotes, cloud services are not required. If you are working on multiple networks, cloud services is highly recommended although not strictly required.