You can't access the gallery. (If my memory is correct you can still save your Sims to your library though I'm not 100% sure) You can't participate in reward events. Other online content like links to surveys and trailers about new packs won't load.
You can test out the experience offline and simply go back online if there's anything you don't like about it. I personally both play online and offline time to time. Like if I'm building today I play online so I can use the gallery. When there're events happening I play online. But if I'm just playing around with my Sims or creating CC I do it offline.