Is it feasible to build and update a WordPress website offline?

It totally depends on the types of changes being made. If you’re modifying a theme or a plugin, depending on what the changes are, you can likely build them locally or on a remote dev server, then push them to production with ease.

That works for a user or two, with more users you need version control – something like Git or SVN – to track and merge changes.

See this: https://stackoverflow.com/questions/9705849/how-to-set-up-a-stageing-enviorment-for-wordpress-wordpress-mu/10837071

I usually prefer to have a remote dev server because it’s easier to replicate the production environment, and it’s easier to access from multiple machines. The way I set it up is no slower than local development… possibly even faster.