New items, events, and features will be introduced via free updates. In addition, if you're playing with somebody else, whether it's local or online, both Switch systems need to have the same ACNH update installed. For these reasons, updating to the latest version (1.1.1 as of the time of this post) is highly recommended.
When it comes to timed events like the Bunny Day event, it should be possible to activate these kinds of events without connecting to Nintendo's online services. For now though, you're right that these kinds of events require an internet connection.