Yes, you do need to connect your booking page to an external calendar for bookings.
YouCanBook.me is not a standalone calendar. We use the existing events on your Google or Microsoft calendar to build a "grid" of available booking times. When you receive a new booking, an event is added to your linked calendar, and YouCanBook.me communicates with that event to trigger emails to you, your team member and your client.
Without connecting a linked calendar to your booking page, your booking page is unable to take bookings.