Navigating discrete UI elements or making simple UI actions of the kind that can be mapped to keyboard input - that’s easily doable with a keyboard. Occasionally it’s just a tad harder with keyboard than with mouse (web pages are notoriously useless with keyboard) but it’s possible.
I wouldn’t last a day without going crazy without a mouse though. People who say they have gone mouseless also seem to argue they have zero 2D input and basically use text and ignore all other workloads. That’s not exactly solving the problem (not that I think it can be solved any better than just using a mouse!)