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. Yes you can play with packs but I don't own all the packs yet and haven't played with all the packs I own.
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.