No, given that one of the points of Outlook (and most email apps) is to store a local archive that can be read even when offline.

Email is older than the internet.

Anyway, no, you don't need internet for the modern version we have today either. You only need it for a few moments.

Some people are being a bit pedantic about not technically needing the internet for email, and that's true, but the pedantry is hiding the fact that actually email is really cool in how it exists in whatever form we want it to be in! It can be transmitted over internet, or over bare TCP/IP, or even peer-to-peer. Most applications don't take advantage of how versatile email really is.

Of course, Micro$oft makes it rely on an always-on internet connection because it's better for their bottom line.

Sorry to see you dog piled for an innocent question. We should see it as a good thing that someone who doesn't know found this space.