If you don't have/refuse a web connection, it will still work, but not have the features of backup/restore of kernel files, etc if needed in case of recovery.
It would be the same issue that people have now; not getting updates, etc...however, many applications might fail to fully work without the web dependency as they might be seen as 'not needed'. Consider this similar to trying to play recent games that REQUIRED a web connection to register/start playing...even offline content.