About your own bookings and events, yes — reminders, a cancellation, a payment recorded or refunded, a nudge to leave a review once a session you were part of is completed, a recap from an event you had a seat at, announcements from communities you belong to, and, for an event you organise, what happens after you publish it: approval, a request for changes, or a takedown. Those are part of the service and you get them because you made a booking.
Anything else only if you ticked the box. It is not ticked for you, it is not required to use openhour, and you can untick it at any time in your profile.