Yes of course. There is an option to make your event either Public or Private when you create your event.
Setting your event as Public means that your event will appear on the Pelago Explore screen and anyone will be able to view and share your event.
If your event is Private, only people you invite to the event will be able to view it, and you can decide whether or not your event can be shared.
You can also edit this setting from your event dashboard whether your event is draft or upcoming, and change the setting from Public to Private or vice versa if you need to. Edit your event and select "Private".